On-line measurement and control of polymer properties by raman spectroscopy

ABSTRACT

Methods are provided for determining and controlling polymer properties on-line in a polymerization reactor system, such as a fluidized bed reactor. The methods include obtaining a regression model for determining a polymer property, the regression model including principal component loadings and principal component scores, acquiring a Raman spectrum of a polyolefin sample comprising polyolefin, calculating a new principal component score from at least a portion of the Raman spectrum and the principal component loadings, and calculating the polymer property by applying the new principal component score to the regression model. The property can be controlled by adjusting at least one polymerization parameter based on the calculated polymer property.

FIELD OF THE INVENTION

[0001] The present invention is directed generally to methods ofmeasuring polymer properties on-line in a polymerization reactor system,and using those measured properties to control the polymerizationreaction. In particular, the present invention provides methods ofmeasuring properties of polyolefins such as melt index and densityon-line, using Raman spectroscopy, and methods of controlling a reactorusing real-time, on-line polymer property data provided by Ramanspectroscopic measurements.

BACKGROUND

[0002] Gas phase processes for the homopolymerization andcopolymerization of monomers, especially olefin monomers, are well knownin the art. Such processes can be conducted, for example, by introducingthe gaseous monomer or monomers into a stirred and/or fluidized bed ofresin particles and catalyst.

[0003] In the fluidized-bed polymerization of olefins, thepolymerization is conducted in a fluidized-bed reactor, wherein a bed ofpolymer particles is maintained in a fluidized state by means of anascending gas stream including gaseous reaction monomer. Thepolymerization of olefins in a stirred-bed reactor differs frompolymerization in a gas fluidized-bed reactor by the action of amechanical stirrer within the reaction zone, which contributes tofluidization of the bed. As used herein, the term “fluidized-bed” alsoincludes stirred-bed processes and reactors.

[0004] The start-up of a fluidized bed reactor generally uses a bed ofpre-formed polymer particles. During the course of polymerization, freshpolymer is generated by the catalytic polymerization of the monomer, andpolymer product is withdrawn to maintain the bed at constant volume. Anindustrially favored process employs a fluidization grid to distributethe fluidizing gas to the bed, and also to act as a support for the bedwhen the supply of gas is cut off. The polymer produced is generallywithdrawn from the reactor via one or more discharge conduits disposedin the lower portion of the reactor, near the fluidization grid. Thefluidized bed includes a bed of growing polymer particles, polymerproduct particles and catalyst particles. This reaction mixture ismaintained in a fluidized condition by the continuous upward flow fromthe base of the reactor of a fluidizing gas which includes recycle gasdrawn from the top of the reactor, together with added make-up monomer.

[0005] The fluidizing gas enters the bottom of the reactor and ispassed, preferably through a fluidization grid, upwardly through thefluidized bed.

[0006] The polymerization of olefins is an exothermic reaction, and itis therefore necessary to cool the bed to remove the heat ofpolymerization. In the absence of such cooling, the bed would increasein temperature until, for example, the catalyst became inactive or thepolymer particles melted and began to fuse.

[0007] In the fluidized-bed polymerization of olefins, a typical methodfor removing the heat of polymerization is by passing a cooling gas,such as the fluidizing gas, which is at a temperature lower than thedesired polymerization temperature, through the fluidized-bed to conductaway the heat of polymerization. The gas is removed from the reactor,cooled by passage through an external heat exchanger and then recycledto the bed.

[0008] The temperature of the recycle gas can be adjusted in the heatexchanger to maintain the fluidized-bed at the desired polymerizationtemperature. In this method of polymerizing alpha olefins, the recyclegas generally includes one or more monomeric olefins, optionallytogether with, for example, an inert diluent gas or a gaseous chaintransfer agent such as hydrogen. The recycle gas thus serves to supplymonomer to the bed to fluidize the bed and to maintain the bed within adesired temperature range. Monomers consumed by conversion into polymerin the course of the polymerization reaction are normally replaced byadding make-up monomer to the recycle gas stream.

[0009] The material exiting the reactor includes the polyolefin and arecycle stream containing unreacted monomer gases. Followingpolymerization, the polymer is recovered. If desired, the recycle streamcan be compressed and cooled, and mixed with feed components, whereupona gas phase and a liquid phase are then returned to the reactor.

[0010] The polymerization process can use Ziegler-Natta and/ormetallocene catalysts. A variety of gas phase polymerization processesare known. For example, the recycle stream can be cooled to atemperature below the dew point, resulting in condensing a portion ofthe recycle stream, as described in U.S. Pat. Nos. 4,543,399 and4,588,790. This intentional introduction of a liquid into a recyclestream or reactor during the process is referred to generally as a“condensed mode” operation.

[0011] Further details of fluidized bed reactors and their operation aredisclosed in, for example, U.S. Pat. Nos. 4,243,619, 4,543,399,5,352,749, 5,436,304, 5,405,922, 5,462,999, and 6,218,484, thedisclosures of which are incorporated herein by reference.

[0012] The properties of the polymer produced in the reactor areaffected by a variety of operating -parameters, such as temperatures,monomer feed rates, catalyst feed rates, and hydrogen gas concentration.In order to produce polymer having a desired set of properties, such asmelt index and density, polymer exiting the reactor is sampled andlaboratory measurements carried out to characterize the polymer. If itis discovered that one or more polymer properties are outside a desiredrange, polymerization conditions can be adjusted, and the polymerresampled. This periodic sampling, testing and adjusting, however, isundesirably slow, since sampling and laboratory testing of polymerproperties such as melt index, molecular weight distribution and densityis time-consuming. As a result, conventional processes can produce largequantities of “off-spec” polymer before manual testing and control caneffectively adjust the polymerization conditions. This occurs duringproduction of a particular grade of resin as well as during thetransition process between grades.

[0013] Methods have been developed to attempt to provide rapidassessment of certain polymer properties and rapid adjustment ofpolymerization conditions. PCT publications WO 01/09201 and WO 01/09203disclose Raman-based methods using principal components analysis (PCA)and partial least squares (PLS) to determine concentrations ofcomponents in a slurry reactor. The concentration of a particularcomponent, such as ethylene or hexene, is determined based onmeasurements of a known Raman peak corresponding to the component. U.S.Pat. No. 5,999,255 discloses a method for measuring a physical propertyof a polymer sample, preferably nylon, by measuring a portion of a Ramanspectrum of the polymer sample, determining a value of a preselectedspectral feature from the Raman spectrum, and comparing the determinedvalue to reference values. This method relies on identification andmonitoring of preselected spectral features corresponding to identifiedfunctional groups, such as NH or methyl, of the polymer.

[0014] Additional background information can be found in U.S. Pat. Nos.6,144,897 and 5,151,474; European Patent application EP 0 561 078; PCTpublication WO 98/08066; and Ardell, G. G. et al., “Model Prediction forReactor Control,” Chemical Engineering Progress, American Institute ofChemical Engineers, U.S., vol. 79, no. 6, Jun. 1, 1983, pages 77-83(ISSN 0360-7275).

[0015] It would be desirable to have methods of determining polymerproperties such as melt index, density and molecular weightdistribution, on-line in a fluidized bed polymerization reactor, withoutthe need to preselect or identify spectral features of a polymer tomonitor. It would also be desirable to have methods of controlling agas-phase fluidized bed reactor to maintain desired polymer properties,based on a rapid, on-line determination of the polymer properties.

SUMMARY OF THE INVENTION

[0016] In one aspect, the present invention provides a process fordetermining polymer properties in a polymerization reactor system. Theprocess includes obtaining a regression model for determining a polymerproperty, the regression model including principal component loadingsand principal component scores, acquiring a Raman spectrum of apolyolefin sample comprising polyolefin, calculating a new principalcomponent score from at least a portion of the Raman spectrum and theprincipal component loadings, and calculating the polymer property byapplying the new principal component score to the regression model.

[0017] In another aspect, the present invention provides a process forcontrolling polymer properties in a polymerization reactor system. Theprocess includes obtaining a regression model for determining a polymerproperty, the regression model including principal component loadingsand principal component scores, acquiring a Raman spectrum of apolyolefin sample comprising polyolefin, calculating a new principalcomponent score from at least a portion of the Raman spectrum and theprincipal component loadings, calculating the polymer property byapplying the new principal component score to the regression model, andadjusting at least one polymerization parameter based on the calculatedpolymer property. In particular embodiments, the at least onepolymerization parameter can be, for example, monomer feed rate,comonomer feed rate, catalyst feed rate, hydrogen gas feed rate, orreaction temperature.

[0018] In one embodiment, the regression model is constructed byobtaining a plurality of Raman spectra of polyolefin samples,calculating principal component loadings and principal component scoresfrom the spectra using principal component analysis (PCA), and formingthe regression model using the principal component scores such that theregression model correlates the polymer property to the principalcomponent scores.

[0019] In another embodiment, the regression model is a locally weightedregression model.

[0020] In another embodiment, the method includes: obtaining a firstregression model for determining a first polymer property, the firstregression model including first principal component loadings and firstprincipal component scores; obtaining a second regression model fordetermining a second polymer property, the second regression modelincluding second principal component loadings and second principalcomponent scores; acquiring a Raman spectrum of a sample comprisingpolyolefin; calculating a new first principal component score from atleast a portion of the Raman spectrum and the first principal componentloadings; calculating a new second principal component score from atleast a portion of the Raman spectrum and the second principal componentloadings; calculating the first polymer property by applying the newfirst principal component score to the first regression model; andcalculating the second polymer property by applying the new secondprincipal component score to the second regression model.

[0021] In another embodiment, the sample includes polyolefin particles.

[0022] In another embodiment, the Raman spectrum is acquired byproviding a sample of polyolefin particles and irradiating the sampleand collecting scattered radiation during a sampling interval using asampling probe, wherein there is relative motion between the sample andthe sampling probe during at least a portion of the sampling interval.The relative motion serves to effectively increase the field of view ofthe sampling probe, providing more accurate data.

[0023] In another embodiment, the polymerization reactor is afluidized-bed reactor.

[0024] In other embodiments, suitable polymer properties include, forexample, density, melt flow rates such as melt index or flow index,molecular weight, molecular weight distribution, and various functionsof such properties.

BRIEF DESCRIPTION OF THE DRAWINGS

[0025]FIG. 1 is a block diagram of a gas-phase reactor.

[0026]FIG. 2 is a block diagram of a Raman analyzer according to theinvention.

[0027]FIG. 3 illustrates one embodiment of a fiber optic Raman probe.

[0028]FIG. 4 illustrates one embodiment of a sample chamber.

[0029]FIG. 5 is a representative Raman spectrum of a granular linear lowpolyethylene polymer sample.

[0030]FIGS. 6a and 6 b show predicted versus measured melt indices inlow and high melt index ranges, respectively, according to Examples 1and 2.

[0031]FIG. 7 shows predicted versus measured density according toExample 3.

[0032]FIGS. 8a and 8 b show predicted versus measured melt indices fromon-man Raman analyses in metallocene- and Ziegler-Natta-catalyzedreactions, respectively, according to Examples 4-5.

[0033]FIGS. 9a and 9 b show predicted versus measured density fromon-line Raman analyses in metallocene- and Ziegler-Natta-catalyzedreactions, respectively, according to Examples 6-7.

[0034]FIG. 10 shows predicted versus measured melt indices from on-lineRaman analyses in a commercial-scale fluidized-bed reactor, over aperiod of about five weeks.

[0035]FIG. 11 shows predicted versus measured densities from on-lineRaman analyses in a commercial-scale fluidized-bed reactor, over aperiod of about five weeks.

DETAILED DESCRIPTION

[0036] In one embodiment, the present invention provides a method ofdetermining polyolefin polymer properties on-line, i.e., as thepolyolefin is produced in a reactor system, without the need forexternal sampling and analysis. The method includes obtaining aregression model for determining a polymer property, the regressionmodel including principal component loadings and principal componentscores, acquiring a Raman spectrum of a polyolefin sample, calculating anew principal component score from at least a portion of the Ramanspectrum and the principal component loadings, and calculating thepolymer property by applying the new principal component score to theregression model.

[0037] In one embodiment, the method is used to determine polymerproperties on-line in a fluidized-bed reactor system. Fluidized-bedreactors are well-known in the art; a particular, non-limiting exampleof a fluidized bed reactor is described herein, for illustrativepurposes only. Those skilled in the art will recognize that numerousmodifications and enhancements can be made, as desired, to thefluidized-bed reactor.

Fluidized-Bed Reactor

[0038]FIG. 1 illustrates a gas-phase fluidized bed reactor 20 having areactor body 22, which is generally an upright cylinder having afluidization grid 24 located in its lower regions. The reactor body 22encloses a fluidized bed zone 26 and a velocity reduction zone 28 whichis generally of increased diameter compared to the diameter of thefluidized bed zone 26 of the reactor body 22.

[0039] The gaseous reaction mixture leaving the top of the reactor body22, the “recycle gas stream,” contains principally unreacted monomer,unreacted hydrogen gas, inert condensable gases such as isopentane, andinert non-condensable gases such as nitrogen. The recycle gas stream istransferred via line 30 to compressor 32, and from compressor 32 to heatexchanger 34. An optional cyclone separator 36 may be used as shown,preferably upstream of compressor 32, to remove fines, if desired. Anoptional gas analyzer 38 can be used if desired, to sample the recyclegas stream to determine concentrations of various components. Typically,the gas analyzer is a gas phase chromatograph (GPC), or a spectrographsuch as a near-infrared spectrometer or a fourier transformnear-infrared spectrometer (FT-NIR). An additional heat exchanger (notshown) may also be used if desired, preferably upstream of compressor32.

[0040] The cooled recycle gas stream exits the heat exchanger 34 vialine 40. As discussed above, the cooled recycle gas stream can begaseous, or can be a mixture of gaseous and liquid phases. FIG. 1 showsan optional configuration wherein at least a portion of the recycle gasstream is cooled to a temperature at or below the temperature whereliquid condensate begins to form (the dew point). All or a portion ofthe resultant gas liquid mixture is transferred via line 40 to aseparator 42, where all or a portion of the liquid is removed. All or aportion of the gas stream, which may contain some liquid, is transferredvia line 44 to a point below the fluidization grid 24 in the lowerregion of the reactor. An amount of upwardly flowing gas, sufficient tomaintain the bed in a fluidized condition, is provided in this way.

[0041] Those skilled in the art will understand that less gas isrequired to maintain fluidization when the reactor employed is a stirredbed reactor.

[0042] An optional compressor 46 may be provided to ensure that asufficient velocity is imparted to the gases flowing through line 44into the bottom of the reactor. The gas stream entering the bottom ofthe reactor may contain condensed liquid, if desired.

[0043] All or a portion of the liquid phase separated from the recyclestream in separator 42 is transferred via line 48 to a manifold 50located at or near the top of the reactor. If desired, a pump 52 may beprovided in line 48 to facilitate the transfer of liquid to manifold 50.The liquid entering manifold 50 flows downward into manifold 54 througha plurality of conduits 56 which have good heat exchange properties andwhich are in heat exchange contact with the wall of the reator. Thepassage of liquid through the conduits 56 cools the interior wall of thereactor and warms the liquid to a greater or lesser extent, dependingupon the temperature differential and the duration and extent of heatexchange contact. Thus by the time the liquid entering manifold 50reaches manifold 54, it has become a heated fluid which may haveremained in an entirely liquid state or it may have become partially ortotally vaporized.

[0044] As shown in FIG. 1, the heated fluid (gas and/or liquid) ispassed from manifold 54 via line 58 to combine with gases leaving theseparator 42 via line 44, prior to entry into the reactor in the regionbelow the fluidization grid 24. In like manner, make-up monomer can beintroduced into the reactor in either liquid or gaseous form via line60. Gas and/or liquid collected in manifold 54 may also be transferreddirectly into the reactor (not shown) in the region below thefluidization grid.

[0045] Product polymer particles can be removed from the reactor vialine 62 in the conventional way, as for example by the method andapparatus described in U.S. Pat. No. 4,621,952. Although only one line62 is shown in the Figure, typical reactors can include more than oneline 62.

[0046] Catalyst is continuously or intermittently injected into thereactor using a catalyst feeder (not shown) such as the device disclosedin U.S. Pat. No. 3,779,712. The catalyst is preferably fed into thereactor at a point 20 to 40 percent of the reactor diameter away fromthe reactor wall and at a height of about 5 to about 30 percent of theheight of the bed. The catalyst can be any catalyst suitable for use ina fluidized bed reactor and capable of polymerizing ethylene, such asone or more metallocene catalysts, one or more Ziegler-Natta catalysts,bimetallilic catalysts, or mixtures of catalysts.

[0047] A gas which is inert to the catalyst, such as nitrogen or argon,is preferably used to carry catalyst into the bed. Cold condensed liquidfrom either separator 42 or from manifold 54 may also be used totransport catalyst into the bed.

[0048] In methods of the present invention, the fluidized bed reactor isoperated to form at least one polyolefin homopolymer or copolymer.Suitable polyolefins include, but are not limited to, polyethylene,polypropylene, polyisobutylene, and homopolymers and copolymers thereof.

[0049] In one embodiment, the at least one polyolefin includespolyethylene homopolymer and/or copolymer. Low density polyethylene(“LDPE”) can be prepared at high pressure using free radical initiators,or in gas phase processes using Ziegler-Natta or vanadium catalysts, andtypically has a density in the range of 0.916-0.940 g/cm³. LDPE is alsoknown as “branched” or “heterogeneously branched” polyethylene becauseof the relatively large number of long chain branches extending from themain polymer backbone. Polyethylene in the same density range, i.e.,0.916 to 0.940 g/cm³, which is linear and does not contain long chainbranching is also known; this “linear low density polyethylene”(“LLDPE”) can be produced with conventional Ziegler-Natta catalysts orwith metallocene catalysts. Relatively higher density LDPE, typically inthe range of 0.928 to 0.940 g/cm³, is sometimes referred to as mediumdensity polyethylene (“MDPE”). Polyethylenes having still greaterdensity are the high density polyethylenes (“HDPEs”), i.e.,polyethylenes having densities greater than 0.940 g/cm³, and aregenerally prepared with Ziegler-Natta catalysts. Very low densitypolyethylene (“VLDPE”) is also known. VLDPEs can be produced by a numberof different processes yielding polymers with different properties, butcan be generally described as polyethylenes having a density less than0.916 g/cm³, typically 0.890 to 0.915 g/cm³ or 0.900 to 0.915 g/cm³.

[0050] Polymers having more than two types of monomers, such asterpolymers, are also included within the term “copolymer” as usedherein. Suitable comonomers include α-olefins, such as C₃-C₂₀ α-olefinsor C₃-C₁₂ α-olefins. The α-olefin comonomer can be linear or branched,and two or more comonomers can be used, if desired. Examples of suitablecomonomers include linear C₃-C₁₂ α-olefins, and α-olefins having one ormore C₁-C₃ alkyl branches, or an aryl group. Specific examples includepropylene; 3-methyl-1-butene; 3,3-dimethyl-1-butene; 1-pentene;1-pentene with one or more methyl, ethyl or propyl substituents;1-hexene with one or more methyl, ethyl or propyl substituents;1-heptene with one or more methyl, ethyl or propyl substituents;1-octene with one or more methyl, ethyl or propyl substituents; 1-nonenewith one or more methyl, ethyl or propyl substituents; ethyl, methyl ordimethyl-substituted 1-decene; 1-dodecene; and styrene. It should beappreciated that the list of comonomers above is merely exemplary, andis not intended to be limiting. Preferred comonomers include propylene,1-butene, 1-pentene, 4-methyl-1-pentene, 1-hexene, 1-octene and styrene.

[0051] Other useful comonomers include polar vinyl, conjugated andnon-conjugated dienes, acetylene and aldehyde monomers, which can beincluded in minor amounts in terpolymer compositions. Non-conjugateddienes useful as co-monomers preferably are straight chain, hydrocarbondiolefins or cycloalkenyl-substituted alkenes, having 6 to 15 carbonatoms. Suitable non-conjugated dienes include, for example: (a) straightchain acyclic dienes, such as 1,4-hexadiene and 1,6-octadiene; (b)branched chain acyclic dienes, such as 5-methyl-1,4-hexadiene;3,7-dimethyl-1,6-octadiene; and 3,7-dimethyl-1,7-octadiene; (c) singlering alicyclic dienes, such as 1,4-cyclohexadiene; 1,5-cyclo-octadieneand 1,7-cyclododecadiene; (d) multi-ring alicyclic fused and bridgedring dienes, such as tetrahydroindene; norbomadiene;methyl-tetrahydroindene; dicyclopentadiene (DCPD);bicyclo-(2.2.1)-hepta-2,5-diene; alkenyl, alkylidene, cycloalkenyl andcycloalkylidene norbomenes, such as 5-methylene-2-norbornene (MNB),5-propenyl-2-norbornene, 5-isopropylidene-2-norbornene,5-(4-cyclopentenyl)-2-norbomene, 5-cyclohexylidene-2-norbomene, and5-vinyl-2-norbornene (VNB); and (e) cycloalkenyl-substituted alkenes,such as vinyl cyclohexene, allyl cyclohexene, vinyl cyclooctene, 4-vinylcyclohexene, allyl cyclodecene, and vinyl cyclododecene. Of thenon-conjugated dienes typically used, the preferred dienes aredicyclopentadiene, 1,4-hexadiene, 5-methylene-2-norbornene,5-ethylidene-2-norbomene, and tetracyclo-(Δ-11,12)-5,8-dodecene.Particularly preferred diolefins are 5-ethylidene-2-norbornene (ENB),1,4-hexadiene, dicyclopentadiene (DCPD), norbomadiene, and5-vinyl-2-norbornene (VNB).

[0052] The amount of comonomer used will depend upon the desired densityof the polyolefin and the specific comonomers selected. One skilled inthe art can readily determine the appropriate comonomer contentappropriate to produce a polyolefin having a desired density.

Raman Spectroscopy

[0053] Raman spectroscopy is a well-known analytical tool for molecularcharacterization, identification, and quantification. Raman spectroscopymakes use of inelastically scattered radiation from a non-resonant,non-ionizing radiation source, typically a visible or near-infraredradiation source such as a laser, to obtain information about molecularvibrational-rotational states. In general, non-ionizing, non-resonantradiation is scattered elastically and isotropically (Raleighscattering) from a scattering center, such as a molecule. Subject towell-known symmetry and selection rules, a very small fraction of theincident radiation can be inelastically and isotropically scattered,with each inelastically scattered photon having an energyE=hυ₀±|E_(i′,j′)−E_(i,j)|, where hυ₀ is the energy of the incidentphoton and |E_(i′,j′)−E_(i,j)| is the absolute difference in energybetween the final (i′,j′) and initial (i,j) vibrational-rotationalstates of the molecule. This inelastically scattered radiation is theRaman scattering, and includes both Stokes scattering, where thescattered photon has lower energy than the incident photon(E=hυ₀−|E_(i′,j′)−E_(i,j)|), and anti-Stokes scattering, where thescattered photon has higher energy than the incident photon(E=hυ₀+|E_(i′,j′−E) _(i,j)|).

[0054] Raman spectra are typically shown as plots of intensity(arbitrary units) versus “Raman shift”, where the Raman shift is thedifference in energy or wavelength between the excitation radiation andthe scattered radiation. The Raman shift is typically reported in unitsof wavenumbers (cm⁻¹), i.e., the reciprocal of the wavelength shift incentimeters. Energy difference |E_(i′,j′)−E_(i,j)| and wavenumbers (co)are related by the expression |E_(i′,j′)−E_(i,j)|=hcω, where h isPlanck's constant, c is the speed of light in cm/s, and ω is thereciprocal of the wavelength shift in centimeters.

[0055] The spectral range of the Raman spectrum acquired is notparticularly limited, but a useful range includes Raman shifts (Stokesand/or anti-Stokes) corresponding to a typical range of polyatomicvibrational frequencies, generally from about 100 cm⁻¹ to about 4000cm⁻¹. It should be appreciated that useful spectral information ispresent in lower and higher frequency regions. For example, numerous lowfrequency molecular modes contribute to Raman scattering in the regionbelow 100 cm⁻¹ Raman shift, and overtone vibrations (harmonics)contribute to Raman scattering in the region above 4000 cm⁻¹ Ramanshift. Thus, if desired, acquisition and use of a Raman spectrum asdescribed herein can include these lower and higher frequency spectralregions.

[0056] Conversely, the spectral region acquired can be less than all ofthe 100 cm⁻¹ to 4000 cm⁻¹ region. For many polyolefins, the majority ofRaman scattering intensity will be present in a region from about 500cm⁻¹ to about 3500 cm⁻¹ or from 1000 cm⁻¹ to 3000 cm⁻¹. The regionacquired can also include a plurality of sub-regions that need not becontiguous.

[0057] As explained below, it is a particular advantage of the methodsdescribed herein that Raman scattering intensity data is useful indetermining properties of polyolefin particles without the need toidentify, select, or resolve particular spectral features. Thus, it isnot necessary to identify a particular spectral feature as being due toa particular mode of a particular moiety of the polyolefin, nor is itnecessary to selectively monitor Raman scattering corresponding to aselected spectral feature. Indeed, it has been surprisingly found thatsuch selective monitoring disadvantageously disregards a wealth ofinformation content embedded in the spectrum that, heretofore, hasgenerally been considered to be merely unusable scattering intensitydisposed between and underlying the identifiable (and thus presumeduseful) bands. Accordingly, in the methods described herein, the Ramanspectral data acquired and used includes a plurality of frequency orwavelength shift, scattering intensity (x, y) measurements overrelatively broad spectral regions, including regions conventionallyidentified as spectral bands and regions conventionally identified asinterband, or unresolved regions.

[0058] The frequency spacing of acquired data can be readily determinedby one skilled in the art, based on considerations of machine resolutionand capacity, acquisition time, data analysis time, and informationdensity. Similarly, the amount of signal averaging used is readilydetermined by one skilled in the art based on machine and processefficiencies and limitations.

[0059] The spectral region measured can include Stokes scattering (i.e.,radiation scattered at frequencies lower than the excitation frequency),anti-Stokes scattering (i.e., radiation scattered at frequencies higherthan the excitation frequency), or both. Optionally, polarizationinformation embedded in the Raman scattering signal can also be used,and one skilled in the art readily understands how to acquire Ramanpolarization information. However, determining polymer properties asdescribed herein does not require the use of polarization information.In some embodiments described herein, any Raman polarization isessentially randomized as a result of interactions with the fiber opticconduit used to convey the signal to the signal analyzer, as describedbelow.

Raman Instrumentation

[0060] Referring now to FIG. 2, the instrumentation used to collect andprocess Raman data includes a Raman subsystem 100, a sample subsystem200, and a data subsystem 300. As shown in FIG. 2, the sample subsystem200 is in communication with reactor 20 via polymer output line 62 (seealso FIG. 1). Each of these subsystems is described below.

Raman Subsystem

[0061] The Raman subsystem includes a Raman spectrometer, the principalcomponents of which are an excitation source 102, a monochromator 104,and a detector 106. Raman spectrometers are well-known analyticalinstruments, and thus only a brief description is provided herein.

[0062] A Raman spectrometer includes an excitation source 102 whichdelivers excitation radiation to the sample subsystem 200. Scatteredradiation is collected within the sample subsystem 200 (describedbelow), filtered of Raleigh scattered light, and dispersed viamonochromator 104. The dispersed Raman scattered light is then imagedonto a detector 106 and subsequently processed in data subsystem 300, asfurther described below.

Excitation Source

[0063] The excitation source and frequency can be readily determinedbased on considerations well-known in the art. Typically, the excitationsource 102 is a visible or near infrared laser, such as afrequency-doubled Nd:YAG laser (532 nm), a helium-neon laser (633 nm),or a solid-state diode laser (such as 785 nm). The laser can be pulsedor continuous wave (CW), polarized as desired or randomly polarized, andpreferably single-mode. Typical excitation lasers will have 100 to 400mW power (CW), although lower or higher power can be used as desired.Light sources other than lasers can be used, and wavelengths and lasertypes and parameters other than those listed above can also be used. Itis well-known that scattering, including Raman scattering, isproportional to the fourth power of the excitation frequency, subject tothe practical limitation that fluorescence typically overwhelms therelatively weak Raman signal at higher frequencies. Thus, higherfrequency (shorter wavelength) sources are preferred to maximize signal,while lower frequency (longer wavelength) sources are preferred tominimize fluorescence. One skilled in the art can readily determine theappropriate excitation source based on these and other considerations,such as mode stability, maintenance time and costs, capital costs, andother factors well understood in the art.

[0064] The excitation radiation can be delivered to the sample subsystem200, and the scattered radiation collected from the sample subsystem, byany convenient means known in the art, such as conventional beammanipulation optics, or fiber optic cables. For an on-line processmeasurement, it is particularly convenient to deliver the excitationradiation and collect the scattered radiation fiber-optically. It is aparticular advantage of Raman spectroscopy that the excitation radiationtypically used is readily manipulated fiber optically, and thus theexcitation source can be positioned remotely from the sampling region. Aparticular fiber optic probe is described below; however, one skilled inthe art will appreciate that the Raman system is not limited to anyparticular means of radiation manipulation.

Monochromator

[0065] The scattered radiation is collected and dispersed by anyconvenient means known in the art, such as a fiber optic probe asdescribed below. The collected scattered radiation is filtered to removeRaleigh scattering and optionally filtered to remove fluorescence, thenfrequency (wavelength) dispersed using a suitable dispersive element,such as a blazed grating or a holographic grating, orinterferometrically (e.g., using Fourier transforms). The grating can befixed or scanning, depending upon the type of detector used. Themonochromator 104 can be any such dispersive element, along withassociated filters and beam manipulation optics.

Detector

[0066] The dispersed Raman scattering is imaged onto a detector 106. Thechoice of detector is easily made by one skilled in the art, taking intoaccount various factors such as resolution, sensitivity to theappropriate frequency range, response time, etc. Typical detectorsinclude array detectors generally used with fixed-dispersivemonochromators, such as diode arrays or charge coupled devices (CCDs),or single element detectors generally used with scanning-dispersivemonochromators, such as lead sulfide detectors andindium-gallium-arsenide detectors. In the case of array detectors, thedetector is calibrated such that the frequency (wavelength)corresponding to each detector element is known. The detector responseis delivered to the data subsystem 300 which generates a set offrequency shift, intensity (x,y) data points which constitute the Ramanspectrum.

Sample Subsystem

[0067] The sample subsystem 200 couples the Raman subsystem 100 to thepolymerization process. Thus, the sample subsystem 200 delivers theexcitation radiation from the excitation source 102 to the polymersample, collects the scattered radiation, and delivers the scatteredradiation to the monochromator 104.

[0068] As noted above, the excitation radiation can be delivered to andcollected from the polymer sample by any convenient means, such as usingconventional optics or fiber optic cables.

[0069] In one embodiment, the sample subsystem includes a probe 204 anda sample chamber 202. FIG. 3 shows a block diagram of one embodiment ofa fiber optic probe. The probe includes a fiber optic bundle 206including one or more fiber optic cables 208 carrying the excitationradiation from the excitation source toward the sample, and one or morefiber optic cables 210 carrying the collected scattered radiation fromthe sample. Fiber optic cables 208 are in optical communication with theexcitation source (102 in FIG. 2), and fiber optic cables 210 are inoptical communication with the monochromator (104 in FIG. 2). Theexcitation and scattered radiation can be manipulated using well-knowntechniques. Thus, it should be appreciated that the particular opticalsetup shown in FIG. 3 is merely exemplary. Excitation radiation 212 isdirected via optics 214 to a holographic grating 216 and spatial filter218 to remove silica Raman due to the fiber optic cable, then directedvia mirror 220 and beam combiner 222 to sampling optics 224 and samplechamber 202. Scattered radiation is collected via sampling optics 224and directed through beam combiner 222, a notch filter 226 to remove theRaleigh scattered radiation, and into fiber optic cables 210.

[0070] The sample in the sample chamber includes a plurality of polymerparticles (granules), and represents the polymer product as dischargedfrom the reactor. Advantageously, it is not necessary that the sample befree of liquid-phase components, such as residual solvent or otherliquid hydrocarbons that may be present in the polymer in the dischargeline of a fluidized-bed reactor.

[0071] Raman probes such as described herein are imaging, in that theyhave a focused field of view. An imaging probe is the most efficientoptical configuration, and because the Raman signal is weak the imagingprobe collects as much scattered light as possible. A disadvantage of animaging probe is that the probe “sees” only a very small amount of thesample at any one time. For a typical fluidized-bed process, a fixedimaging probe has a field of view corresponding to only 1 or 2 polymergranules. Thus, the data collected in a static mode may not berepresentative of the bulk material.

[0072] In one embodiment, the disadvantage of a limited field of view isovercome by providing relative motion between the sample and the Ramanprobe, so that the probe collects scattering from many polymer granulesover the course of the sampling interval. Thus, for example, the probecan be moved through the sample during at least a portion of thesampling interval or, equivalently, the sample or sample chamber can bemoved relative to a fixed probe during at least a portion of thesampling interval, or both can be moved. In a particular embodiment, itis convenient to keep the sample chamber stationary and move the Ramanprobe into and out of the sample chamber during the sampling interval bylinearly translating the probe using a linear actuator. One skilled inthe art will readily appreciate, however, that relative motion betweenthe sample granules and the probe can be achieved by numerous othermechanisms, such as, for example, allowing polymer granules to pass by astationary probe.

[0073] As a specific example, a particular sampling system used inExamples 4-7 below is now described. It should be appreciated that thisparticular system is exemplary and not limiting.

[0074] A fluidized-bed polymerization plant having two reactors wasused, with one reactor producing metallocene-catalyzed LLDPE resin, andthe other reactor producing Ziegler-Natta catalyzed LLDPE resin.Referring now to FIG. 4, each reactor 20 (only one reactor shown) hastwo dump valves A and B that alternate to remove product from thereactor. The product is pneumatically conveyed through product dischargepipe 62 with 90 psi (0.6 MPa) nitrogen at a speed of about 60 miles perhour (0.4 m/s). At this speed the slug of product dumped from a reactorwill only be present at any one point in the pipe for a few seconds.However, it is preferred to average the Raman signal for 60-120 secondsto improve the signal-to-noise ratio. To accomplish this, a small amountof product (about 800 grams) is trapped and held in a sample chamber 202as the slug passes through the product discharge pipe 62. The samplechamber 202 is attached to the product discharge pipe 62 by a 1 inch (25mm) diameter pipe 62 b and a pneumatically actuated valve C or D. Theoperation of the valves C and D is controlled by the Raman analyzer, butcould also be controlled by an auxiliary system. The Raman analyzerwaits for a signal from the reactor telling it that the dump valve A orB has opened. The Raman analyzer then opens valve C or D connecting thesample chamber 202 to the product discharge pipe 62, and waits for atime predetermined to be sufficient to have allowed the slug of productto have passed by the sample capture point. The Raman analyzer nextcloses the sample capture valve C or D, trapping the captured sample ofproduct in the sample chamber 202.

[0075] The Raman analyzer probe 204 includes a probe head 230 enclosingthe filtering and optical (not electronic) signal processing elements,and a sample interface 232, which is an 8” long by 0.5” diameter (20cm×1.3 cm) tube. Tube 232 is inserted through the end of the samplechamber opposite to where the sample enters, so that it comes in contactwith the sample. A pneumatic linear actuator 234 is attached to theprobe 204 to slowly draw the probe out of the sample chamber and thenreinsert it during a sample collection interval. This probe movementcauses sample to flow across the front of the probe, providing acontinually changing sample for measurement.

[0076] The reactor 20 dumps on a 3-6 minute cycle (grade dependent),alternating between 2 lines 62 controlled by valves A and B. Sample iscollected from only one of the lines. The sample system operates bywaiting for a Sample Ready signal from the reactor telling the Ramananalyzer that a sample is being dumped. The Sample Ready signal is inthe form of a digital input to the Raman analyzer. When the analyzerreceives the Sample Ready signal, there is a sequence of tasks itperforms prior to setting up the valves for the Capture Sampleoperation, which are:

[0077] Check to determine if the Sample Ready is for the next stream. Inthe Raman control software, there is a stream sequence list that theoperator sets to tell the analyzer which reactor(s) to sample andmeasure. Typically, this would be 1,2,1,2, etc., for a two reactorsystem, but under some circumstances such as a grade transition onreactor 1, the operator might want to sample, for example,1,1,1,2,1,1,1,2, etc. Thus, the analyzer checks to make sure the dumpindicator it receives is consistent with the current stream sequence. Ifnot, the analyzer ignores the signal.

[0078] Check that the Reactor On-line digital input for this reactor isvalid. The typical stream sequence 1,2,1,2 . . . may be in effect, butthe operator may decide to only monitor a single reactor, such as duringa transition or upset. The reactor receives separate digital inputs foreach reactor, which tell it whether or not to sample a particularreactor regardless of the active or current stream sequence list.

[0079] Wait a set time interval between the Sample Ready signal andsetting valves for Capture Sample.

[0080] Set Valves for Capture Sample.

[0081] The valve states are shown in the table below for a sequencesampling through the A valve of product discharge line 62, with state“C” being closed, and state “O” being open. Valve States For SamplingValve A B C D E F Waiting for Sample C C C C C C Capture Sample O C O OC C Measure Spectrum C C C C C O Eject Sample C C O C O O Reset Probe CC O C O C

[0082] Sample Capture is accomplished by opening the sample chambervalves C and D. In the configuration where product is discharged throughthe A valve of product discharge line 62, an open valve C permits thesample to enter sample chamber 202, and an open valve D serves as avent. A portion of the discharged polymer product in 90 psig nitrogenbeing transported at about 60 miles per hour packs into the samplechamber 202 attached to a bend in the product discharge line 62. Oncethe sample chamber 202 is full, the analyzer performs a series ofoperations to complete data collection and prepare for the next sample.These operations include:

[0083] Wait a specified time interval after the Capture Sample valvestate is set.

[0084] Set the Measure Spectrum valve state.

[0085] Eject the sample

[0086] Reset the Probe Position.

[0087] Set the Waiting for Sample valve state

[0088] Update the stream sequence information.

[0089] The probe is attached to linear actuator so that it can be movedin and out of the sample chamber. In the Waiting for Sample state (5),the probe is fully inserted into the sample chamber so that the shaft ofthe probe is immersed in sample after the chamber is filled. The MeasureSpectrum valve state (2) not only closes valves C and D, but alsoactuates both three-way valves controlling the linear actuator so thatthe probe is slowly extracted from the sample chamber while data isbeing collected. Upon completion of the Spectrum Collect operation, thesample in the sample chamber is ejected back into the sample transportline by opening valves C and E.

Data Subsystem

[0090] Referring again to FIG. 2, the data subsystem includes ananalyzer 302, which receives the response signal of the detector 106.The analyzer can be, for example, a computer capable of storing andprocessing the Raman data. Other functions of the analyzer can include,for example, developing the regression model and carrying out PCA/LWRanalysis, as described below. In one embodiment described above, thedata subsystem controls the motion of the sampling probe. In anotherembodiment described above, the data subsystem controls valves forfilling and emptying the sample chamber. In another embodiment, the datasubsystem compares the calculated value of one or more polymerproperties to a target value, and adjusts one or more reactor parametersin response to the deviation between calculated and target values.Reactor control is further described below.

PCA/LWR Analysis

[0091] The Raman spectrum includes information directly or indirectlyrelated to various properties of the polyolefin sample. Conventionally,sample components are identified by the presence of unique spectralsignatures, such as particular bands recognized as being due toparticular vibrational modes of a molecule. Quantitative informationsuch as concentration can then be obtained about a sample component by,for example, integrating the area under a particular peak and comparingthe area to a calibration sample, by monitoring scattered intensity at aparticular peak as a function of time, etc. In contrast to theseconventional approaches, the present inventors have surprisingly foundthat polymer properties can be determined from Raman spectra without theneed to identify or select particular spectral features, by using amultivariate model to correlate polymer properties with Raman scatteringdata. The model uses large, contiguous regions of the spectrum, ratherthan discrete spectral bands, thereby capturing large amounts ofinformation density unavailable and unrecognized in conventionalanalysis. Further, the spectral data are correlated to polymerproperties such as melt flow rates (defined below), densities, molecularweight distributions, etc., that are not readily apparent from opticalspectra.

[0092] In one embodiment, the data analysis described below is used tobuild and apply a predictive model for at least one property of thepolyolefin particles selected from melt flow rate, density, molecularweight, molecular weight distribution, and functions thereof.

[0093] As used herein, the term “melt flow rate” indicates any of thevarious quantities defined according to ASTM D-1238, including I_(2.16),the melt flow rate of the polymer measured according to ASTM D-1238,condition E (2.16 kg load, 190 ° C.), commonly termed the “melt index”,and I_(21.6), the melt flow rate of the polymer measured according toASTM D-1238, condition F (21.6 kg load, 190 ° C.), commonly termed the“flow index.” Other melt flow rates can be specified at differenttemperatures or different loads. The ratio of two melt flow rates is the“Melt Flow Ratio” or MFR, and is most commonly the ratio ofI_(21.6)/I_(2.16). “MFR” can be used generally to indicate a ratio ofmelt flow rates measured at a higher load (numerator) to a lower load(denominator).

[0094] As used herein, “molecular weight” indicates any of the momentsof the molecular weight distribution, such as the number average, weightaverage, or Z-average molecular weights, and “molecular weightdistribution” indicates the ratio of two such molecular weights. Ingeneral, molecular weights M can be computed from the expression:$M = \frac{\sum\limits_{i}{N_{i}M_{i}^{n + 1}}}{\sum\limits_{i}{N_{i}M_{i}^{n}}}$

[0095] where N_(i) is the number of molecules having a molecular weightM_(i). When n=0, M is the number average molecular weight Mn. When n=1,M is the weight average molecular weight Mw. When n=2, M is theZ-average molecular weight Mz. These and higher moments are included inthe term “molecular weight.” The desired molecular weight distribution(MWD) function (such as, for example, Mw/Mn or Mz/Mw) is the ratio ofthe corresponding M values. Measurement of M and MWD by conventionalmethods such as gel permeation chromatography is well known in the artand is discussed in more detail in, for example, Slade, P. E. Ed.,Polymer Molecular Weights Part II, Marcel Dekker, Inc., NY, (1975)287-368; Rodriguez, F., Principles of Polymer Systems 3rd ed.,Hemisphere Pub. Corp., NY, (1989) 155-160; U.S. Pat. No. 4,540,753;Verstrate et al., Macromolecules, vol. 21, (1988) 3360; and referencescited therein.

[0096] Methods of the invention include obtaining a regression model fordetermining a polymer property, the regression model including principalcomponent loadings and principal component scores; acquiring a Ramanspectrum of a polyolefin sample; calculating a new principal componentscore from at least a portion of the Raman spectrum and the principalcomponent loadings; and calculating the polymer property by applying thenew principal component score to the regression model.

[0097] The regression model is preferable a locally weighted regression(LWR) model, using principal component analysis (PCA) eigenvectors. PCAis a well-known analytical method, and is described, for example, inPirouette™ Multivariate Data Analysis for Windows software manual,Infometrix, Inc, Woodinville, Wash. (1985-2000), PLS_Toolbox™ softwaremanual, Eigenvector Research, Inc., Manson, Wash. (1998), and referencescited therein. LWR is described, for example, in Naes and Isaksson,Analytical Chemistry, 62, 664-673 (1990), Sekulic et al., AnalyticalChemistry, 65, 835A-845A (1993), and references cited therein.

[0098] Principal Components Analysis is a mathematical method whichforms linear combinations of raw variables to construct a set ofmutually orthogonal eigenvectors (principal component loadings). Sincethe eigenvectors are mutually orthogonal, these new variables areuncorrelated. Further, PCA can calculate the eigenvectors in order ofdecreasing variance. Although the analysis computes a number ofeigenvectors equal to the number of original variables, in practice, thefirst few eigenvectors capture a large amount of the sample variance.Thus, only a relatively small number of eigenvectors is needed toadequately capture the variance, and a large number of eigenvectorscapturing minimal variance can be disregarded, if desired.

[0099] The data are expressed in an m (row) by n (column) matrix X, witheach sample being a row and each variable a column optionally meancentered, autoscaled, scaled by another function or not scaled. Thecovariance of the data matrix, cov(X), can be expressed as:

cov(X)=X ^(T) X/(m−1)

[0100] where the superscript T indicates the transpose matrix. The PCAanalysis decomposes the data matrix as a linear combination of principalcomponent scores vectors S_(i) and principal component loading vectors(eigenvectors) L_(i), as follows:

X=S ₁ L _(i) ^(T) +S ₂ L ₂ ^(T) +S ₃ L ₂ ^(T)+. . .

[0101] The eigenvectors L_(i) are eigenvectors of the covariance matrix,with the corresponding eigenvalues λ_(i) indicating the relative amountof covariance captured by each eigenvector. Thus, the linear combinationcan be truncated after the sum of the remaining eigenvalues reaches anacceptably small value.

[0102] A model can be constructed correlating the Raman scatteringintensity with a polymer property in PCA space using various linear ornonlinear mathematical models, such as principal components regression(PCR), partial least squares (PLS), projection pursuit regression (PPR),alternating conditional expectations (ACE), multivariate adaptiveregression splines (MARS), and neural networks (NN), to name a few.

[0103] In a particular embodiment, the model is a locally weightedregression model. Locally Weighted Regression (LWR) assumes that asmooth non-linear function can be approximated by a linear or relativelysimple non-linear (such as quadratic) function, with only the closestdata points being used in the regression. The q closest points are usedand are weighted by proximity, and the regression model is applied tothe locally weighted values.

[0104] In the calibration phase, Raman spectra are acquired, and thepolymer properties of the sample are measured in the laboratory. Theproperties measured include those that the model will predict, such asdensity, melt flow rates, molecular weights, molecular weightdistributions, and functions thereof. For a desired polymer property,the data set including the measured polymer properties the samples andthe Raman spectral data for the samples is decomposed into PCA space toobtain a calibration data set. No particular number of calibrationsamples is required. One skilled in the art can determine theappropriate number of calibration samples based on the performance ofthe model and the incremental change in performance with additionalcalibration data. Similarly, there is no particular number of PCAeigenvectors required, and one skilled in the art can choose anappropriate number based on the amount of variance captured a selectednumber of eigenvectors and the incremental effect of additionaleigenvectors.

[0105] The LWR model can be validated using methods known in the art. Itis convenient to divide the calibration samples into two sets: acalibration data set, and a validation data set. The calibration dataset is used to develop the model, and to predict the appropriate polymerproperty for the samples in the validation data set, using thevalidation data set Raman spectra. Since the chosen polymer property forthe validation data set samples is both calculated and measured, theeffectiveness of the model can be evaluated by comparing the calculatedand measured values.

[0106] The validated model can then be applied to sample spectra topredict the desired polymer property or properties.

[0107] If desired, a single model can be used to predict two or morepolymer properties. Preferably, separate models are developed for eachpolymer property. Thus, in one embodiment, the present inventionincludes: obtaining a first regression model for determining a firstpolymer property, the first regression model including first principalcomponent loadings and first principal component scores; obtaining asecond regression model for determining a second polymer property, thesecond regression model including second principal component loadingsand second principal component scores; acquiring a Raman spectrum of asample comprising polyolefin; calculating a new first principalcomponent score from at least a portion of the Raman spectrum and thefirst principal component loadings; calculating a new second principalcomponent score from at least a portion of the Raman spectrum and thesecond principal component loadings; calculating the first polymerproperty by applying the new first principal component score to thefirst regression model; and calculating the second polymer property byapplying the new second principal component score to the secondregression model.

[0108] Of course, more than two polymer properties can be determined byincluding third or more regression models. Advantageously, multiplepolymer properties can be determined essentially simultaneously by usingthe same Raman spectrum and applying several regression models to thespectral data.

[0109] In a particular embodiment, two regression models are used, andboth a melt flow rate (such as melt index I_(2.16) or flow indexI_(21.6)) and density are determined.

Reaction Control

[0110] In one embodiment, the calculated polymer property is compared toa target polymer property, and at least one reactor parameter isadjusted based on the deviation between the calculated and targetpolymer property. The at least one reactor parameter can include theamounts of monomer, comonomer, catalyst and cocatalyst, the operatingtemperature of the reactor, the ratio of comonomer(s) to monomer, theratio of hydrogen to monomer or comonomer, and other parameters thataffect the chosen polymer property. For example, if the chosen polymerproperty is density and the density calculated from the PCA/LWR model islower than a target density, a reactor parameter can be adjusted toincrease density, such as, for example, reducing the comonomer feed rateand/or increasing the monomer feed rate.

[0111] For example, in the case of the fluidized bed polymerization ofolefins, hydrogen can serve as a chain transfer agent. In this way, themolecular weight of the polymer product can be controlled. Additionally,varying the hydrogen concentration in olefin polymerization reactors canalso vary the polymer melt flow rate, such as the melt index I_(2.16)(MI). The present invention allows control of the reactor to producepolymer having a selected MI range. This is accomplished by knowing therelationship between hydrogen concentration and the MI of polymersproduced by a specific reactor, and programming the target MI or MIrange into a reactor control system processor. By monitoring the polymerMI data generated by the Raman analyzer and comparing this data to thetarget MI range, the flow of hydrogen into the reactor vessel may beadjusted so that the MI range of the polymer product remains within thetarget MI range.

[0112] It will be understood by those skilled in the art that otherreactor constituent properties and other reactor parameters can be used.In a similar way as described above, the final polymer properties may beachieved by controlled metering reactor parameters in response to datagenerated by the Raman analyzer.

EXAMPLES

[0113] Laboratory determinations of density (g/cm³) used a compressionmolded sample, cooled at 15° C. per hour and conditioned for 40 hours atroom temperature according to ASTM D1505 and ASTM D1928, procedure C.

[0114] Laboratory determinations of melt flow rates were carried out at190° C. according to ASTM D-1238. I_(21.6) is the “flow index” or meltflow rate of the polymer measured according to ASTM D-1238, condition F,and I_(2.16) is the “melt index” or melt flow rate of the polymermeasured according to ASTM D-1238, condition E. The ratio of I_(21.6) toI_(2.16) is the “melt flow ratio” or “MFR”.

[0115] EXCEED™ 350 is a gas-phase metallocene produced LLDPEethylene/hexene copolymer with a Melt Index (I_(2.16)) of 1.0 g/10 min,and a density of 0.918 g/cm³, available from ExxonMobil Chemical Co.,Houston, Tex. The EXCEED™ 350 resin is now marketed as EXCEED™ 3518.

[0116] EXCEED™ 357 is a gas-phase metallocene produced LLDPEethylene/hexene copolymer with a Melt Index (I_(2.16)) of 3.4 g/10 min,and a density of 0.917 g/cm³, available from ExxonMobil Chemical Co.,Houston, Tex. The EXCEED™ 357 resin is now marketed as EXCEED™ 3518.

[0117] ExxonMobil LL-1002 is a gas-phase Ziegler-Natta produced LLDPEethylene/butene copolymer resin having a Melt Index (I_(2.16)) of 2.0g/l 0 min, and a density of 0.918 g/cm³, available from ExxonMobilChemical Co., Houston, Tex.

[0118] ExxonMobil LL-1107 is a gas-phase Ziegler-Natta produced LLDPEethylene/butene copolymer resin having a Melt Index (I2.16) of 0.8 g/10min, and a density of 0.922 g/cm³, available from ExxonMobil ChemicalCo., Houston, Tex.

[0119] ExxonMobil LL-6100 is a gas-phase Ziegler-Natta produced LLDPEethylene/butene copolymer resin having a Melt Index (I_(2.16)) of 20g/10 min, and a density of 0.925 g/cm³, available from ExxonMobilChemical Co., Houston, Tex.

[0120] ExxonMobil LL-6101 is a gas-phase Ziegler-Natta produced LLDPEethyleneibutene copolymer resin having a Melt Index (I_(2.16)) of 20g/10 min, and a density of 0.925 g/cm³, available from ExxonMobilChemical Co., Houston, Tex.

[0121] ExxonMobil LL-6201 is a gas-phase Ziegler-Natta produced LLDPEethylene/butene copolymer resin having a Melt Index (I_(2.16)) of 50g/10 min, and a density of 0.926 g/cm³, available from ExxonMobilChemical Co., Houston, Tex.

Examples 1-3

[0122] Examples 1-3 were used to show the feasibility of embodiments ofthe invention. In Examples 1-3, measurements were made in thelaboratory, simulating the measurements that would be made on-line in apolymerization reactor.

[0123] The Raman system used for Examples 1-3 was a Kaiser OpticalHoloprobe Process Raman Analyzer, available from Kaiser Optical Systems,Inc., Ann Arbor, Michigan. The Raman system used a 125 mW diode laseroperating at 785 nm, and was equipped with a probe with 2.5 (6.3 cm)inch imaging optics fiber-optically coupled to the instrument, aholographic notch filter, holographic dispersion grating, cooled CCDdetector (−40° C.), and computer for analyzer control and data analysis.A more complete description of this commercial instrument can be foundin “Electro-Optic, Integrated Optic, and Electronic Technologies forOnline Chemical Process Monitoring,” Proceedings SPIE, vol. 3537, pp.200-212 (1998), the disclosure of which is incorporated herein byreference for purposes of U.S. patent practice.

[0124] Data collection was accomplished by positioning the Raman probeabove the surface of a polymer granule sample at a distance of about 2.5inches (6.3 cm). The probe was fiber optically coupled to the Ramananalyzer for both excitation and scattering signals. Data were collectedfrom each sample for three minutes (i.e., signal averaged for 3minutes). The CCD detector is sensitive to cosmic rays, which can causespurious signals in array elements. “Cosmic ray checking” is a detectorfunction that checks for these artifacts and discards them. In thefollowing examples, the cosmic ray checking function was used.

[0125] Raman spectra were collected over the region of 100 to 3500 cm⁻¹.Three consecutive spectra were collected for each sample used. Thesamples were obtained from either of two gas-phase fluidized bedreactors producing copolymers of ethylene and butene or hexene, usingmetallocene catalysts. Laboratory measurements of melt index and/ordensity were also made for each sample.

[0126] The data were divided into calibration sets, used to develop thePCA/LWR models, and validation sets, used to evaluate the accuracy ofthe model. Separate models were developed for a relatively low meltindex range, a relatively high melt index range, and density.

Example 1 Low Melt Index Model

[0127] Seventy-three polymer samples were evaluated. The samples weredivided into a group of 50 used for calibration (model development) anda group of 23 used for model validation. Each sample was ametallocene-catalyzed LLDPE resin, with hexene comonomer, in a meltindex range of from about 0.6 to about 1.2 g/10 min. Raman spectra andlaboratory melt index measurements were collected as described above.

[0128] The lab values of melt index and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for low range melt index, using principal component loadings andprincipal component scores. The measured melt indexes, predicted meltindexes, and deviations (i.e., deviation of the actual melt index fromthe prediction of the LWR model) are shown in Table 1. TABLE 1 Low MICalibration MI (Lab) MI (Model) ΔMI^((a)) (dg/min) (dg/min) (dg/min)0.678 0.663401 −0.0146 0.678 0.675728 −0.00227 0.679 0.685591 0.0065910.679 0.653462 −0.02554 0.687 0.699942 0.012942 0.687 0.709433 0.0224330.696 0.700481 0.004481 0.696 0.696309 0.000309 0.7 0.689811 −0.010190.7 0.694658 −0.00534 0.705 0.690562 −0.01444 0.705 0.706591 0.0015910.706 0.69476 −0.01124 0.706 0.718346 0.012346 0.714 0.706535 −0.007460.714 0.703178 −0.01082 0.7546 0.786602 0.032002 0.7546 0.7746160.020016 0.772 0.781622 0.009622 0.772 0.779611 0.007611 0.773 0.7751320.002132 0.773 0.777378 0.004378 0.808 0.800435 −0.00757 0.808 0.8248230.016823 0.82 0.825021 0.005021 0.82 0.823629 0.003629 0.831 0.8414780.010478 0.831 0.8089 −0.0221 0.84 0.819804 −0.0202 0.84 0.838078−0.00192 0.92 0.934314 0.014314 0.92 0.93859 0.01859 1.06 1.049136−0.01086 1.06 1.07161 0.01161 1.07 1.080271 0.010271 1.07 1.0797010.009701 1.08 1.090437 0.010437 1.08 1.055101 −0.0249 1.098 1.1173670.019367 1.098 1.092972 −0.00503 1.1 1.083835 −0.01617 1.1 1.071211−0.02879 1.11 1.115756 0.005756 1.11 1.106827 −0.00317 1.11 1.085486−0.02451 1.11 1.096664 −0.01334 1.15 1.142874 −0.00713 1.15 1.1283−0.0217 1.1811 1.200165 0.019065 1.1811 1.198869 0.017769

[0129] The Raman spectra of the validation data set were collected, andnew principal component scores were calculated from the validationspectra. Using the locally-weighted regression model, the melt index ofeach validation sample was then calculated. The measured melt indexes,predicted melt indexes, and deviations (i.e., deviation of the actualmelt index from the prediction of the LWR model) are shown in Table 2.TABLE 2 Low MI Validation MI (Lab) MI (Model) ΔMI^((a)) (dg/min)(dg/min) (dg/min) 0.55 0.561835 0.011835 0.55 0.579349 0.029349 0.550.57315 0.02315 0.616 0.654254 0.038254 0.616 0.637083 0.021083 0.6160.667328 0.051328 0.622 0.6504 0.0284 0.622 0.635863 0.013863 0.6220.669156 0.047156 0.679 0.644011 −0.03499 0.679 0.632626 −0.04637 0.6790.634522 −0.04448 0.883 0.802692 −0.08031 0.883 0.856272 −0.02673 0.8830.849839 −0.03316 0.95 1.083123 0.133123 0.95 1.022883 0.072883 0.951.021329 0.071329 1.065 1.006358 −0.05864 1.065 0.950208 −0.11479 1.0650.978949 −0.08605 1.142 1.14752 0.00552 1.142 1.12363 −0.01837

[0130]FIG. 6A depicts the data from Tables 1 and 2 graphically. The linein the Figure is the model prediction. The calculated R² value was 0.99for the calibration set, with a standard error of 0.0155, and 0.92 forthe validation set, with a standard error of 0.059.

Example 2 High Melt Index Model

[0131] An analysis was carried out as in Example 1, using higher meltindex samples. Thirty-four polymer samples were evaluated. These sampleswere used as calibration samples for model development, but a validationsubset was not used. Each sample was a metallocene-catalyzed LLDPEresin, with butene comonomer, in a melt index range of from about 4 toabout 60 g/10 min. Raman spectra and laboratory melt index measurementswere collected as described above.

[0132] The lab values of melt index and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for high range melt index, using principal component loadings andprincipal component scores. The measured melt indexes, predicted meltindexes, and deviations (i.e., deviation of the actual melt index fromthe prediction of the LWR model) are shown in Table 3. TABLE 3 High MICalibration MI (Lab) MI (Model) ΔMI^((a)) (dg/min) (dg/min) (dg/min)4.341 4.513 0.172 4.341 4.467 0.126 8.613 8.433 −0.18 8.613 8.314 −0.29910.499 9.978 −0.521 10.499 10.768 0.269 12.547 13.013 0.466 12.54712.971 0.424 18.61 17.955 −0.655 18.61 17.885 −0.725 19.81 21.009 1.19919.81 20.893 1.083 21.59 22.011 0.421 21.59 22.314 0.724 22.79 22.291−0.499 22.79 23.109 0.319 30.68 28.212 −2.468 30.68 29.118 −1.562 32.9332.112 −0.818 32.93 32.459 −0.471 33.68 34.658 0.978 33.68 34.233 0.55336.6 37.216 0.616 36.6 36.989 0.389 45.15 44.433 −0.717 45.15 45.001−0.149 48.07 48.966 0.896 48.07 49.207 1.137 51.41 49.879 −1.531 51.4150.554 −0.856 55.56 57.213 1.653 55.56 56.667 1.107 57.41 57.942 0.53257.41 58.217 0.807

[0133]FIG. 6B depicts the data from Table 3 graphically. The line in theFigure is the model prediction. The calculated R² value was 0.99, with astandard error of 0.91.

Example 3 Density Model

[0134] An analysis was carried out as in Example 1, using density ratherthan melt index as the predicted property. A subset of 22 of the polymersamples used in Example 1 were evaluated. These samples were used ascalibration samples for model development, but a validation subset wasnot used. Each sample was a metallocene-catalyzed LLDPE resin, withhexene comonomer. Raman spectra and laboratory density measurements werecollected as described above.

[0135] The lab values of density and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for density, using principal component loadings and principalcomponent scores. The measured densities, predicted densities, anddeviations (i.e., deviation of the actual density from the prediction ofthe LWR model) are shown in Table 4. TABLE 4 Density Calibration ρ (Lab)ρ (Model) ρ^((a)) (g/cm³) (g/cm³) (g/cm³) 0.9183 0.919018 0.0007180.9183 0.919053 0.000753 0.9185 0.917859 −0.00064 0.9185 0.917786−0.00071 0.9195 0.918575 −0.00092 0.9195 0.918499 −0.001 0.9196 0.919342−0.00026 0.9196 0.919943 0.000343 0.9212 0.921674 0.000474 0.92120.921701 0.000501 0.9218 0.92193 0.00013 0.9218 0.922121 0.000321 0.9220.921901 −0.000099 0.922 0.922797 0.000797 0.9226 0.921872 −0.000730.9226 0.922369 −0.00023 0.9244 0.924316 −0.000084 0.9244 0.924075−0.00033 0.9249 0.924893 −0.000007 0.9249 0.924031 −0.00087 0.92620.926252 0.000052 0.9262 0.925936 −0.00026

[0136]FIG. 7 depicts the data graphically. The line in the Figure is themodel prediction. The calculated R² value was 0.95, with a standarderror of 0.00057.

Examples 4-5

[0137] Examples 4-5 demonstrate the effectiveness of the inventivemethods on-line in a polymerization reaction system, for melt indexdetermination.

[0138] The Raman system used for Examples 4-5 was as described forExamples 1-3, except that the laser was a 200 mW mode-stabilized diodelaser operating at 785 nm. Polymer samples from either of two gas-phasefluidized-bed reactors were taken using the sampling system describedabove.

[0139] The data were divided into calibration sets, used to develop thePCA/LWR models, and validation sets, used to evaluate the accuracy ofthe model. Separate models were developed for a melt index (Examples4-5) and density (Examples 6-7). In addition, separate models weredeveloped for each of the two gas-phase reactors. The two reactors aredenoted “Reactor 1” and “Reactor 2” below.

Example 4 Melt Index Model, Reactor 1

[0140] Two hundred eighty-five polymer samples were evaluated. Thesamples were divided into a group of 216 used for calibration (modeldevelopment) and a group of 69 used for model validation. Each samplewas a metallocene-catalyzed LLDPE resin, in a melt index range of fromless than 1 to about 15 g/10 min. Raman spectra and laboratory meltindex measurements were collected as described above.

[0141] The lab values of melt index and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for melt index, using principal component loadings and principalcomponent scores. The measured melt indexes and predicted melt indexesare shown in Tables 5A-5B. The deviations are not shown in the table,but are readily calculated from the tabulated data. The data are shownin the order taken (by column, within each table), to illustrate theeffectiveness of the model under changing polymer conditions. A symbol“Vn” before an entry indicates that the nth set of validation spectrawere taken before the marked entry, as shown by the correspondingnotation in Table 6. Table 5B is a continuation of Table 5A. TABLE 5A MICalibration, Reactor 1 MI MI MI (Lab) (Model) MI (Lab) MI (Model) MI(Lab) (Model) (dg/min) (dg/min) (dg/min) (dg/min) (dg/min) (dg/min)4.997 5.013 3.506 3.440 0.967 0.973 4.413 4.390 3.554 3.401 0.952 0.9614.559 4.410 3.554 3.474 0.956 0.977 3.511 3.633 3.541 3.540 0.969 0.9403.481 3.521 3.576 3.713 0.973 0.994 3.315 3.391 3.576 3.679 0.946 0.9803.301 3.286 3.630 3.664 0.972 0.960 3.369 3.211 3.630 3.664 1.135 1.0833.460 3.607 3.626 3.563 1.188 1.209 3.391 3.481 3.618 3.652 1.182 1.2313.380 3.301 3.346 3.257 1.130 1.104 3.523 3.629 3.409 3.399 1.138 1.1933.370 3.294 3.409 3.426 1.015 0.996 3.537 3.522 ^((V1))3.411 3.342 0.9770.967 3.534 3.559 3.572 3.743 0.965 0.973 3.432 3.407 2.351 2.402 0.9700.980 3.518 3.671 1.544 1.574 0.985 0.990 3.555 3.562 1.348 1.364 0.9520.962 3.380 3.299 1.163 1.140 0.923 0.918 3.320 3.308 1.106 1.095 0.9210.900 3.470 3.523 1.072 1.100 1.017 0.981 3.380 3.405 1.098 1.103 1.0051.061 3.380 3.277 1.071 1.110 1.010 1.012 3.370 3.328 0.987 0.971 1.0301.078 3.370 3.400 1.009 0.994 0.986 0.979 3.354 3.290 1.005 0.998 0.9440.937 3.354 3.540 0.978 0.980 0.947 0.953 3.523 3.327 1.009 1.010 0.9550.972 3.523 3.473 0.991 1.039 0.932 0.928 3.491 3.551 1.002 0.991 0.9470.944 3.582 3.613 1.038 1.094 0.984 0.990 3.582 3.612 1.035 1.000 0.9720.994 3.493 3.464 1.016 1.023 0.998 0.990 3.493 3.375 0.940 0.932 0.9911.039 3.523 3.596 0.970 0.980 1.060 1.004 3.506 3.483 0.980 0.979 1.0411.013

[0142] TABLE 5B MI Calibration, Reactor 1, continued MI MI MI (Lab)(Model) MI (Lab) MI (Model) MI (Lab) (Model) (dg/min) (dg/min) (dg/min)(dg/min) (dg/min) (dg/min) 0.989 1.000 0.938 0.942 3.490 3.311 0.9210.910 0.988 0.960 3.528 3.466 0.908 0.880 1.006 1.039 3.538 3.555 0.9510.962 0.982 1.002 3.592 3.403 0.976 0.990 0.946 0.978 3.372 3.441 0.9650.941 0.964 0.930 ^((V4))3.580 3.726 0.970 0.992 1.010 0.962 3.259 3.1090.966 1.002 1.030 1.082 3.302 3.319 0.998 1.092 1.040 1.019 3.437 3.5720.983 0.963 1.080 1.103 3.397 3.429 0.985 0.973 1.020 1.031 3.449 3.4010.990 0.999 1.040 1.039 3.513 3.329 0.990 1.024 ^((V3))1.061 1.092 3.7713.702 0.993 1.003 1.546 1.552 3.986 3.918 0.968 0.982 2.043 1.993 4.5754.428 0.997 0.971 2.381 2.402 5.000 4.892 1.006 0.982 2.751 2.772 6.0546.203 ^((V2))0.939 0.926 3.054 2.994 7.452 7.624 0.966 0.953 3.414 3.5408.392 8.012 0.992 1.017 3.342 3.254 10.630 10.171 0.989 0.993 3.5503.453 10.630 10.171 0.951 0.937 3.580 3.429 12.530 12.779 1.030 1.0183.550 3.445 13.110 13.671 1.000 1.005 3.610 3.454 13.879 13.698 0.9590.939 3.528 3.310 13.952 13.498 0.954 0.957 3.246 3.152 13.627 13.5930.940 0.910 3.523 3.391 13.295 12.998 0.985 0.991 3.620 3.662 13.39313.876 0.980 0.991 3.691 3.604 13.146 13.029 0.955 0.931 3.713 3.70012.810 13.014 0.930 0.909 3.451 3.619 11.989 11.903 0.910 0.891 3.4393.293 10.670 11.003 0.940 0.963 3.501 3.701 12.181 12.292 0.980 1.0033.263 3.331 12.711 12.625 0.980 0.993 3.433 3.383 1.120 1.204 0.9600.968 3.477 3.579 1.002 1.002

[0143] The Raman spectra of the validation data set were also collected,and new principal component scores were calculated from the validationsample was locally-weighted regression model, the melt index of eachvalidation sample was then calculated. The measured and predicted meltindexes are shown in Table 6. Acquisition of the validation spectra wasinterspersed with acquisition of the calibration spectra, at thecorresponding “Vn” positions. TABLE 6 MI Validation, Reactor 1 MI MI MI(Lab) (Model) MI (Lab) MI (Model) MI (Lab) (Model) (dg/min) (dg/min)(dg/min) (dg/min) (dg/min) (dg/min) V1: 3.471 3.514 0.965 0.991 0.9330.960 3.443 3.503 1.000 0.973 0.859 0.811 3.438 3.371 0.995 0.999 0.9340.903 3.493 3.421 0.964 0.952 0.980 1.011 3.417 3.561 0.934 0.943 0.9100.880 3.354 3.365 0.946 0.967 0.890 0.920 3.454 3.604 0.943 0.920 0.9000.899 3.531 3.594 0.928 0.892 0.970 0.992 3.557 3.500 0.931 0.950 0.9800.962 3.521 3.498 0.967 0.972 0.990 1.053 3.440 3.352 0.949 0.957 V4:3.470 3.625 3.507 3.521 1.025 0.980 3.620 3.772 3.596 3.569 1.029 1.0893.420 3.400 3.659 3.623 1.032 1.012 3.504 3.387 3.554 3.648 1.025 1.0343.682 3.598 3.565 3.662 0.999 1.004 3.597 3.784 3.605 3.807 0.995 0.9703.531 3.724 3.573 3.531 1.009 0.998 3.399 3.412 3.456 3.604 1.035 1.0293.590 3.498 3.501 3.586 1.048 1.011 3.520 3.500 3.500 3.398 1.012 1.0293.431 3.548 V2: 0.980 0.998 V3: 1.095 1.118 3.391 3.293 0.966 0.9821.114 1.092 3.288 3.412

[0144]FIG. 8A depicts the data from Tables 5A, 5B and 6 graphically. Theline in the Figure is the model prediction. The calculated R² value was0.999, with a standard error of 2.78%.

Example 5 Melt Index Model, Reactor 2

[0145] The procedure described in Example 4 was followed, except asnoted, sampling this time from the Reactor 2 polymer. Two hundredninety-one polymer samples were evaluated. The samples were divided intoa group of 266 used for calibration (model development) and a group of25 used for model validation. Each sample was a Ziegler-Natta-catalyzedLLDPE resin, in a melt index range of from less than 1 to about 60 g/10min. Raman spectra and laboratory melt index measurements were collectedas described above.

[0146] The lab values of melt index and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for melt index, using principal component loadings and principalcomponent scores. The measured melt indexes and predicted melt indexesare shown in Tables 7A-7B. The deviations are not shown in the table,but are readily calculated from the tabulated data. The data are shownin the order taken (by column, within each table), to illustrate theeffectiveness of the model under changing polymer conditions. A symbol“Vn” before an entry indicates that the nth set of validation spectrawere taken before the marked entry, as shown by the correspondingnotation in Table 8. Table 7B is a continuation of Table 7A. In Tables7A and 7B, the units of melt index (MI) are dg/min. TABLE 7A MICalibration, Reactor 2 MI MI MI MI MI MI (Lab) MI (Model) (Lab) (Model)(Lab) (Model) (Lab) MI (Model) 0.678 0.669 0.890 0.862 53.370 54.00722.150 21.888 2.008 2.105 0.837 0.843 52.750 52.559 21.230 20.465 1.4101.376 ^(V1)17.580 18.001 50.660 51.032 20.440 21.055 0.992 0.988 19.19418.899 51.720 50.759 20.370 20.477 0.832 0.859 20.280 21.021 48.53047.667 19.974 20.077 0.758 0.780 19.588 20.091 44.160 45.221 22.93022.374 0.712 0.688 19.732 18.979 47.000 46.821 ^(V4)7.250 7.442 0.6730.690 20.910 22.098 53.370 54.202 3.790 3.801 0.670 0.710 20.070 20.47341.750 40.512 2.460 2.404 0.721 0.690 19.800 19.070 48.360 49.848 2.0901.998 0.753 0.774 20.900 20.078 50.890 49.111 2.298 2.303 0.751 0.77922.080 21.874 43.810 43.084 1.947 1.887 0.780 0.810 20.080 19.659 43.85044.106 1.830 1.867 0.811 0.779 19.616 19.223 46.200 47.485 2.059 1.9780.792 0.810 19.829 19.629 48.220 48.944 2.131 1.992 0.782 0.750 17.09017.651 49.950 49.004 2.051 2.119 0.753 0.775 18.086 17.888 49.590 50.6722.170 2.085 0.767 0.798 17.638 16.844 ^(V3)41.540 41.094 2.090 2.1770.706 0.700 18.637 17.974 21.320 22.445 2.160 2.285 0.878 0.892 20.01020.119 17.983 18.241 2.130 1.951 0.858 0.823 19.568 19.103 17.233 16.8692.050 1.989 0.817 0.829 ^(V2)27.270 27.906 19.677 19.311 2.000 1.9990.857 0.802 42.780 43.099 19.063 19.921 1.917 1.974 0.849 0.836 48.56047.956 19.919 19.107 1.974 2.101 0.779 0.750 51.950 52.302 21.510 21.4442.064 2.001 0.765 0.770 51.270 51.037 20.840 20.771 2.077 1.985 0.7420.727 49.950 50.119 20.500 19.295 2.035 2.103 0.806 0.800 45.610 46.11720.230 21.011 2.007 2.110 0.810 0.801 47.440 46.938 21.230 20.659 1.9802.004 0.827 0.839 53.620 52.476 21.670 20.997 1.950 1.891 0.778 0.78955.210 54.998 20.590 21.264 1.880 1.871 0.796 0.763 50.010 49.483 23.14022.784 1.990 2.109 0.768 0.712 44.040 44.884 22.460 21.997 2.230 2.1900.899 0.912 42.780 41.009 20.640 20.883 2.100 1.962 0.946 0.963 47.94047.444 21.260 20.799 1.998 2.119 0.965 1.002 53.720 52.798 19.856 20.2311.910 1.967

[0147] TABLE 7B MI Calibration, Reactor 2, continued MI MI MI MI MI MIMI MI (Lab) (Model) (Lab) (Model) (Lab) (Model) (Lab) (Model) 2.2042.187 0.974 0.980 2.010 1.992 1.242 1.219 2.350 2.410 0.992 1.006 1.3461.375 1.320 1.331 2.201 2.177 0.924 0.898 0.945 0.972 1.396 1.387 2.0501.939 0.983 0.978 0.700 0.700 1.480 1.520 2.120 2.098 0.970 0.952 0.8250.830 1.594 1.554 2.000 2.079 1.079 1.108 0.843 0.852 1.525 1.501 2.0402.101 1.077 0.997 0.792 0.804 1.576 1.629 2.100 2.008 1.093 1.121 0.7910.801 1.664 1.711 2.040 2.113 1.108 1.110 0.796 0.799 1.544 1.557 1.9501.889 1.071 0.997 0.745 0.756 1.962 1.891 ^(V5)0.945 0.902 1.013 0.9990.777 0.791 5.093 4.894 0.970 0.978 0.980 0.980 0.734 0.720 9.130 9.2970.965 0.954 1.061 1.046 0.711 0.720 12.063 11.999 1.281 1.299 1.0051.018 0.763 0.777 13.815 13.684 1.445 1.455 0.961 0.967 0.778 0.80113.262 13.555 1.502 1.552 1.005 0.997 0.685 0.673 16.134 16.643 1.3731.299 0.980 0.977 0.769 0.776 15.180 15.322 1.365 1.399 0.864 0.8770.760 0.743 15.845 16.015 1.420 1.390 0.891 0.903 0.738 0.750 15.73015.926 1.462 1.442 0.996 1.043 0.726 0.701 12.221 12.442 1.674 1.7391.054 1.044 0.719 0.742 11.531 11.735 1.868 1.920 1.017 1.009 0.7060.688 12.532 12.221 2.168 2.122 1.023 0.995 0.781 0.743 12.358 12.4711.979 1.948 2.079 1.997 0.797 0.822 12.538 12.882 3.279 3.309 1.9632.047 0.750 0.770 12.549 12.555 0.969 1.002 1.963 2.065 0.779 0.78812.948 12.507 1.018 1.040 1.880 1.841 0.806 0.810 13.413 13.119 1.0781.039 2.070 2.109 0.768 0.773 12.543 12.629 1.009 0.988 2.180 2.1160.896 0.910 12.500 12.409 1.034 0.992 2.290 2.341 1.142 1.172 12.11112.427 1.005 1.056 2.150 2.098 1.176 1.149 11.957 11.883

[0148] The Raman spectra of the validation data set were also collected,and new principal component scores were calculated from the validationspectra. Using the locally-weighted regression model, the melt index ofeach validation sample was then calculated. The measured and predictedmelt indexes are shown in Table 8. Acquisition of the validation spectrawas interspersed with acquisition of the calibration spectra, at thecorresponding “Vn” positions. TABLE 8 MI Validation, Reactor 2 MI MI MI(Lab) MI MI (Lab) (Model) MI (Lab) (Model) (dg/ (Model) (dg/min)(dg/min) (dg/min) (dg/min) min) (dg/min) V1: 0.733 0.771 17.291 17.73823.390 22.991 0.754 0.782 17.896 18.229 V5: 1.915 1.907 0.798 0.81020.620 20.046 1.908 1.946 0.727 0.718 V3: 52.180 51.199 1.958 1.9760.721 0.750 52.020 54.219 1.902 1.911 V2: 17.649 18.223 V4: 24.88024.521 1.930 1.979 18.399 18.519 20.760 20.008 1.930 1.947 19.844 19.49218.667 18.903 21.480 21.018 16.682 16.822

[0149]FIG. 8B depicts the data from Tables 7A, 7B and 8 graphically. Theline in the Figure is the model prediction. The calculated R² value was0.997, with a standard error of 2.86%.

Examples 6-7

[0150] Examples 6-7 demonstrate the effectiveness of the inventivemethods on- line in a polymerization reaction system, for densitydetermination.

[0151] The measurements were carried out as described above inconnection with Examples 4-5, except that a PCA/LWR model was developedfor density. The samples used, and spectra acquired, are a subset ofthose of Examples 4-5. Laboratory measurements of density were made onthe samples in addition to the melt index measurements described above.

Example 6 Density Model, Reactor 1

[0152] One hundred forty-six polymer samples were evaluated. The sampleswere divided into a group of 109 used for calibration (modeldevelopment) and a group of 37 used for model validation. Each samplewas a metallocene-catalyzed LLDPE resin, in a density range of fromabout 0.912 to about 0.921 g/cm³. Raman spectra and laboratory densitymeasurements were collected as described above.

[0153] The lab values of density and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for density, using principal component loadings and principalcomponent scores. The measured densities and predicted densities areshown in Table 9. The deviations are not shown in the table, but arereadily calculated from the tabulated data. The data are shown in theorder taken (by column, within each table), to illustrate theeffectiveness of the model under changing polymer conditions. A symbol“Vn“before an entry indicates that the nth set of validation spectrawere taken before the marked entry, as shown by the correspondingnotation in Table 10. TABLE 9 Density (ρ, g/cm³) Calibration, Reactor 1ρ(Lab) ρ(Model) ρ(Lab) ρ(Model) ρ(Lab) ρ(Model) 0.9202 0.9203 0.91580.9159 0.9151 0.9150 0.9203 0.9199 0.9153 0.9154 0.9158 0.9158 0.91880.9186 0.9161 0.9162 0.9155 0.9157 0.9202 0.9200 0.9189 0.9186^(v3)0.9155 0.9159 0.9196 0.9191 0.9201 0.9205 0.9186 0.9190 0.91960.9195 0.9202 0.9204 0.9181 0.9184 0.9195 0.9196 0.9201 0.9199 0.91930.9195 0.9190 0.9195 0.9208 0.9208 0.9191 0.9194 0.9192 0.9187 0.92010.9202 0.9181 0.9182 0.9195 0.9193 0.9164 0.9166 0.9169 0.9170 0.91950.9199 0.9158 0.9162 0.9189 0.9190 0.9190 0.9194 0.9160 0.9158 0.91810.9180 0.9190 0.9184 0.9159 0.9163 0.9182 0.9184 0.9187 0.9184 0.91570.9160 0.9186 0.9185 0.9187 0.9190 0.9157 0.9156 0.9188 0.9192 0.91880.9190 0.9159 0.9157 0.9186 0.9181 0.9196 0.9192 0.9157 0.9156 0.91840.9185 0.9196 0.9195 0.9161 0.9156 ^(v4)0.9194 0.9197 0.9202 0.91960.9160 0.9163 0.9188 0.9186 0.9202 0.9202 0.9159 0.9154 0.9187 0.91850.9207 0.9204 0.9155 0.9158 0.9180 0.9180 0.9200 0.9199 0.9149 0.91460.9144 0.9147 0.9200 0.9199 0.9156 0.9153 0.9128 0.9130 0.9197 0.92000.9164 0.9162 0.9130 0.9133 0.9195 0.9200 0.9160 0.9164 0.9135 0.91330.9195 0.9193 0.9162 0.9164 0.9141 0.9143 ^(v1)0.9195 0.9199 ^(v2)0.91530.9155 0.9149 0.9151 0.9192 0.9187 0.9160 0.9163 0.9149 0.9151 0.91600.9161 0.9158 0.9161 0.9163 0.9164 0.9155 0.9157 0.9154 0.9151 0.91670.9164 0.9164 0.9159 0.9157 0.9157 0.9168 0.9170 0.9167 0.9171 0.91490.9145 0.9168 0.9173 0.9162 0.9165 0.9153 0.9154 0.9155 0.9161 0.91560.9153 0.9161 0.9165 0.9166 0.9167 0.9156 0.9160 0.9150 0.9153 0.91730.9175 0.9162 0.9165 0.9155 0.9152 0.9159 0.9162 0.9150 0.9151

[0154] The Raman spectra of the validation data set were also collected,and new principal component scores were calculated from the validationspectra. Using the locally-weighted regression model, the density ofeach validation sample was then calculated. The measured and predicteddensities are shown in Table 10. Acquisition of the validation spectrawas interspersed with acquisition of the calibration spectra, at thecorresponding “Vn” positions. TABLE 10 Density (ρ, g/cm³) Validation,Reactor 1 ρ(Lab) ρ(Model) ρ(Lab) ρ(Model) ρ(Lab) ρ(Model) V1: 0.91990.9202 0.9160 0.9159 0.9149 0.9147 0.9205 0.9202 0.9155 0.9152 V4:0.9191 0.9193 0.9205 0.9207 0.9158 0.9155 0.9182 0.9184 0.9199 0.91980.9157 0.9153 0.9192 0.9193 0.9200 0.9198 0.9158 0.9158 0.9197 0.91960.9196 0.9195 0.9157 0.9154 0.9196 0.9200 0.9200 0.9199 0.9158 0.91560.9195 0.9196 0.9198 0.9201 0.9158 0.9153 0.9189 0.9185 0.9190 0.9187V3: 0.9157 0.9160 0.9192 0.9192 0.9195 0.9192 0.9149 0.9150 0.91980.9197 V2: 0.9159 0.9161 0.9168 0.9168 0.9192 0.9193 0.9188 0.91880.9149 0.9146 0.9159 0.9161 0.9150 0.9153

[0155]FIG. 9A depicts the data from Tables 9 and 10 graphically. Theline in the Figure is the model prediction. The calculated R² value was0.978, with a standard error of 0.00028 g/cm³.

Example 7 Density Model, Reactor 2

[0156] The procedure described in Example 6 was followed, except asnoted, sampling this time from the Reactor 2 polymer. One hundredsixty-four polymer samples were evaluated. The samples were divided intoa group of 151 used for calibration (model development) and a group of13 used for model validation. Each sample was a Ziegler-Natta-catalyzedLLDPE resin, in a density range of from about 0.916 to about 0.927g/cm³. Raman spectra and laboratory density measurements were collectedas described above.

[0157] The lab values of density and the Raman spectra of thecalibration data set were used to create a locally-weighted regressionmodel for density, using principal component loadings and principalcomponent scores. The measured densities and predicted densities areshown in Tables 11A-11B. The deviations are not shown in the table, butare readily calculated from the tabulated data. The data are shown inthe order taken (by column, within each table), to illustrate theeffectiveness of the model under changing polymer conditions. A symbol“Vn” before an entry indicates that the nth set of validation spectrawere taken before the marked entry, as shown by the correspondingnotation in Table 12. Table 11B is a continuation of Table 11A. TABLE11A Density (ρ, g/cm³) Calibration, Reactor 2 ρ(Lab) ρ(Model) ρ(Lab)ρ(Model) ρ(Lab) ρ(Model) 0.9182 0.9182 ^(v2)0.9269 0.9270 0.9181 0.91840.9180 0.9184 0.9267 0.9268 0.9180 0.9178 0.9207 0.9209 0.9259 0.92630.9180 0.9179 0.9220 0.9225 0.9246 0.9249 0.9176 0.9180 0.9220 0.92210.9235 0.9235 0.9178 0.9182 0.9220 0.9217 0.9246 0.9250 0.9178 0.91790.9218 0.9219 0.9248 0.9246 0.9190 0.9187 0.9218 0.9219 0.9256 0.92570.9197 0.9192 0.9217 0.9217 0.9251 0.9253 0.9184 0.9178 0.9220 0.92200.9246 0.9246 0.9184 0.9190 0.9226 0.9221 0.9253 0.9253 0.9199 0.91980.9217 0.9216 0.9260 0.9259 0.9182 0.9186 0.9219 0.9222 0.9265 0.92680.9177 0.9174 0.9225 0.9224 0.9265 0.9264 0.9180 0.9178 0.9221 0.92230.9261 0.9260 ^(v4)0.9159 0.9161 0.9216 0.9217 0.9251 0.9256 0.91690.9169 0.9218 0.9219 0.9252 0.9254 0.9173 0.9177 0.9218 0.9213 0.92490.9254 0.9172 0.9176 0.9216 0.9220 0.9257 0.9255 0.9178 0.9181^(v1)0.9268 0.9262 0.9252 0.9247 0.9181 0.9187 0.9256 0.9259 0.92440.9249 0.9179 0.9174 0.9254 0.9254 0.9245 0.9245 0.9204 0.9204 0.92550.9257 0.9250 0.9248 0.9174 0.9180 0.9252 0.9253 0.9256 0.9260 0.91830.9185 0.9247 0.9253 0.9256 0.9260 0.9184 0.9180 0.9255 0.9260^(v3)0.9216 0.9213 0.9177 0.9176 0.9250 0.9246 0.9168 0.9153 0.91730.9169 0.9264 0.9267 0.9184 0.9186 0.9176 0.9174 0.9259 0.9258 0.91910.9189 0.9178 0.9181 0.9253 0.9250 0.9188 0.9187 0.9180 0.9181 0.92470.9245 0.9185 0.9186 0.9182 0.9185

[0158] TABLE 11B Density (ρ, g/cm³) Calibration, Reactor 2, continuedρ(Lab) ρ(Model) ρ(Lab) ρ(Model) ρ(Lab) ρ(Model) 0.9182 0.9185 0.92070.9203 0.9253 0.9253 0.9166 0.9170 0.9213 0.9213 0.9253 0.9253 0.91870.9185 0.9218 0.9215 0.9265 0.9269 0.9184 0.9189 0.9226 0.9231 0.92610.9263 0.9181 0.9183 0.9221 0.9225 0.9259 0.9257 0.9182 0.9177 0.92180.9217 0.9257 0.9257 0.9181 0.9180 0.9216 0.9217 0.9260 0.9255 0.91850.9182 0.9223 0.9218 0.9251 0.9252 0.9180 0.9183 0.9223 0.9220 0.92380.9236 0.9182 0.9187 0.9222 0.9227 0.9248 0.9243 0.9183 0.9187 0.92200.9218 0.9270 0.9275 0.9183 0.9188 0.9223 0.9224 0.9247 0.9243 0.91800.9185 0.9222 0.9223 0.9244 0.9241 0.9181 0.9177 0.9220 0.9218 0.92440.9239 0.9180 0.9183 0.9224 0.9223 0.9249 0.9245 0.9182 0.9182 0.92240.9221 0.9250 0.9246 0.9179 0.9177 0.9225 0.9223 0.9248 0.9246 0.91820.9178 0.9223 0.9220 0.9250 0.9256 0.9181 0.9182 0.9216 0.9216 0.92040.9202 0.9253 0.9253

[0159] The Raman spectra of the validation data set were also collected,and new principal component scores were calculated from the validationspectra. Using the locally-weighted regression model, the melt index ofeach validation sample was then calculated. The measured and predictedmelt indexes are shown in Table 12. Acquisition of the validationspectra was interspersed with acquisition of the calibration spectra, atthe corresponding “Vn” positions. TABLE 12 Density (ρ, g/cm³)Validation, Reactor 2 ρ(Lab) ρ(Model) ρ(Lab) ρ(Model) ρ(Lab) ρ(Model)V1: 0.9216 0.9217 0.9262 0.9265 0.9184 0.9181 0.9221 0.9219 0.92500.9256 0.9185 0.9183 0.9220 0.9218 V3: 0.9238 0.9243 0.9185 0.9188 V2:0.9254 0.9257 0.9228 0.9230 0.9250 0.9247 V4: 0.9182 0.9180

[0160]FIG. 9B depicts the data from Tables 11A, 11B and 12 graphically.The line in the Figure is the model prediction. The calculated R² valuewas 0.989, with a standard error of 0.00034 g/cm³.

Examples 8-9

[0161] Examples 8-9 demonstrate the effectiveness, precision andaccuracy of processes of the invention to predict melt index and densityon-line, in a commercial-scale fluidized-bed polymerization reactor. TheRaman system was as described above but used a 400 mW diode laseroperating at 785 nm. The fiber optic cable used to couple the electricalcomponents of the instrument to the Raman probe (approximately 150 mdistant) was a 62 μm excitation/100 μm collection step index silicafiber.

[0162] Melt index and density models were developed by continuouslycollecting, and saving Raman data as individual spectra every 3-10minutes, on each of two reactors. Validation of each model wasaccomplished by then using the model on- line to determine the polymerproperties.

Example 8

[0163] Polymer melt index was predicted on-line in a commercial-scalefluidized-bed reactor forming various grades of polyethylene copolymer.The prediction was carried out approximately every 12 minutes for about5 weeks. Nearly 500 samples were also tested the laboratory, using thestandard ASTM D-1238, condition E (2.16 kg load, 190° C.) protocol. Theresults, are shown in Table 13, where “MI model” indicates the meltindex 12.16 predicted by the model, and “MI lab” indicates the valueobtained in the laboratory by the ASTM method. The same data are showngraphically in FIG. 10, except that the Figure also shows the predictedMI for samples not corresponding to lab measurements. The predicted MIvalues are spaced sufficiently closely in time that they appear in theFigure to be a line. TABLE 13 Time MI model MI lab (days) (dg/min)(dg/min) 0.009 0.958 0.957 0.086 1.016 1.020 0.155 1.036 1.030 0.2581.007 0.998 0.327 1.002 0.996 0.404 0.982 1.006 0.499 0.941 0.927 0.5850.944 0.940 0.654 1.017 1.015 0.748 1.033 1.037 0.826 0.985 0.989 0.9030.940 0.970 0.998 0.953 0.930 1.084 0.944 0.950 1.161 0.971 0.980 1.2041.073 1.060 1.247 1.220 1.210 1.290 1.373 1.360 1.324 1.461 1.460 1.3671.502 1.520 1.419 1.486 1.506 1.995 2.763 2.770 2.081 2.650 2.650 2.1592.766 2.810 2.236 2.777 2.590 2.339 2.738 2.740 2.399 2.799 2.800 2.5112.970 2.971 2.546 3.056 3.072 2.580 3.235 3.226 2.666 3.427 3.423 2.7523.542 3.545 2.838 3.619 3.699 2.907 3.593 3.580 3.001 3.446 3.380 3.0793.514 3.500 3.165 3.705 3.710 3.242 3.702 3.710 3.337 3.710 3.710 3.3973.713 3.710 3.509 3.478 3.482 3.578 3.421 3.361 3.664 3.466 3.465 3.7503.430 3.443 3.836 3.458 3.459 3.913 3.306 3.300 3.999 3.301 3.290 4.0423.411 3.220 4.085 3.466 3.460 4.171 3.751 3.730 4.248 3.713 3.700 4.3343.493 3.500 4.403 3.497 3.460 4.498 3.459 3.406 4.584 3.516 3.528 4.6703.544 3.555 4.747 3.601 3.616 4.833 3.612 3.593 4.902 3.514 3.536 4.9973.560 3.559 5.091 3.584 3.677 5.177 3.583 3.350 5.255 3.531 3.554 5.3323.473 3.476 5.409 3.528 3.521 5.504 3.537 3.526 5.581 3.484 3.436 5.6673.532 3.592 5.753 3.482 3.516 5.839 3.505 3.516 5.900 3.516 3.464 6.0033.455 3.464 6.080 3.466 3.394 6.166 3.468 3.439 6.252 3.666 3.655 6.3303.723 3.714 6.407 3.712 3.778 6.510 3.578 3.555 6.588 3.483 3.480 6.6653.454 3.470 6.751 3.399 3.540 6.854 3.379 3.360 6.906 1.824 1.810 6.9491.157 1.140 7.000 0.899 0.860 7.043 0.888 0.883 7.086 0.937 0.940 7.1291.001 0.980 7.164 1.053 1.060 7.250 1.105 1.110 7.336 1.083 1.070 7.4131.051 1.040 7.508 1.003 1.010 7.585 0.975 0.973 7.680 0.958 0.950 7.7490.999 0.960 7.835 1.026 1.000 7.903 1.004 1.000 7.998 1.022 1.033 8.1011.038 1.037 8.161 1.021 1.025 8.265 0.968 0.990 8.325 0.992 0.988 9.4600.812 0.754 9.503 0.787 0.790 9.546 0.886 0.871 9.580 0.992 0.989 9.6660.996 0.991 9.752 1.012 1.020 9.830 1.006 1.020 9.899 1.024 1.010 10.0021.127 1.110 10.088 1.016 0.990 10.165 1.051 1.030 10.243 1.062 1.08010.329 1.130 1.130 10.397 1.052 1.010 10.501 1.057 1.040 10.578 1.1311.130 10.664 1.130 1.140 10.750 1.141 1.100 10.836 1.099 1.130 10.9051.121 1.140 10.999 1.057 1.000 11.042 1.107 1.085 11.085 1.314 1.30211.120 1.451 1.426 11.163 1.497 1.495 11.249 1.444 1.458 11.326 1.3741.255 11.395 1.462 1.468 11.507 1.412 1.340 11.584 1.385 1.400 11.6701.364 1.370 11.748 1.332 1.330 11.834 1.370 1.370 11.868 1.675 1.68011.911 2.443 2.431 11.963 3.017 3.029 11.997 3.102 3.107 12.040 3.2073.201 12.083 3.357 3.350 12.126 3.323 3.248 12.169 3.330 3.333 12.2463.505 3.482 12.332 3.491 3.211 12.401 3.691 3.691 12.504 3.713 3.66012.582 4.040 4.080 12.668 3.947 3.960 12.754 3.775 3.770 12.805 3.7433.730 12.840 3.698 3.600 12.900 3.753 3.770 12.960 3.964 3.950 13.0033.693 3.150 13.029 3.501 3.510 13.081 3.112 3.110 13.132 3.063 2.87013.167 3.523 3.520 13.210 3.624 3.630 13.253 3.580 3.600 13.296 3.7063.720 13.330 3.700 3.700 13.459 3.222 3.220 13.502 3.188 3.180 13.5453.234 3.240 13.579 3.256 3.250 13.622 3.313 3.290 13.674 3.327 3.35013.751 3.404 3.350 13.837 3.488 3.550 13.898 3.421 3.390 14.001 3.4253.440 14.087 3.487 3.500 14.164 3.459 3.480 14.250 3.429 3.420 14.3453.373 3.380 14.396 3.363 3.370 14.500 3.420 3.259 14.586 3.467 3.46214.663 3.566 3.400 14.749 3.478 3.475 14.826 3.383 3.409 14.904 3.3233.341 14.998 3.636 3.640 15.084 3.537 3.550 15.170 3.369 3.360 15.2563.270 3.300 15.334 3.644 3.630 15.394 3.289 3.310 15.497 3.136 3.15015.583 3.439 3.435 15.661 3.460 3.448 15.755 3.461 3.494 15.833 3.4663.447 15.901 3.612 3.620 16.005 3.458 3.450 16.039 3.301 3.310 16.0823.222 3.220 16.125 2.997 2.980 16.168 2.804 2.790 16.211 2.751 2.74016.254 2.372 2.390 16.288 2.360 2.360 16.331 2.387 2.400 16.400 2.4672.350 16.495 2.569 2.564 16.581 2.609 2.610 16.667 2.680 2.660 16.7102.649 2.638 16.744 2.074 2.079 16.796 1.916 1.938 16.830 1.917 1.99516.865 1.960 1.967 16.899 2.049 2.070 16.994 2.211 2.200 17.080 2.1522.150 17.166 2.322 2.320 17.252 2.352 2.240 17.329 2.342 2.340 17.3982.239 2.247 17.501 2.110 2.112 17.587 2.081 2.080 17.664 2.098 2.11917.750 2.147 2.130 17.836 2.273 2.301 17.905 2.202 2.205 18.000 2.0582.050 18.086 2.002 2.080 18.163 2.043 2.040 18.249 2.094 2.110 18.3352.203 2.180 18.395 2.260 2.250 18.490 2.264 2.257 18.662 2.292 2.27718.757 2.195 2.158 18.843 2.208 2.189 18.903 2.112 2.139 18.963 1.6761.690 18.997 1.390 1.400 19.040 1.219 1.240 19.083 1.103 1.080 19.1261.125 1.080 19.169 1.077 1.100 19.255 1.030 1.060 19.341 1.019 1.01019.393 0.997 1.050 19.505 0.926 0.927 19.539 0.875 0.886 19.582 0.6050.604 19.617 0.563 0.542 19.660 0.482 0.502 19.746 0.550 0.551 19.8320.575 0.581 19.900 0.562 0.545 19.995 0.541 0.539 20.090 0.568 0.57420.167 0.593 0.572 20.253 0.620 0.585 20.330 0.526 0.530 20.399 0.5000.506 20.511 0.557 0.529 20.580 0.506 0.511 20.657 0.538 0.526 20.7520.533 0.526 20.838 0.516 0.516 20.898 0.531 0.536 21.000 0.509 0.54321.095 0.523 0.522 21.163 0.594 0.542 21.249 0.479 0.530 21.327 0.5150.520 21.404 0.960 0.920 21.456 1.040 1.056 21.499 1.156 1.133 21.5421.152 1.172 21.585 1.157 1.080 21.671 1.005 1.124 21.748 1.090 1.06721.834 1.060 1.036 21.894 1.090 1.091 21.998 1.060 1.110 22.041 1.2091.230 22.084 1.548 1.650 22.135 2.062 2.110 22.170 2.106 2.110 22.2212.066 2.120 22.247 2.108 2.050 22.324 2.117 2.080 22.402 2.155 2.32022.496 2.156 2.190 22.582 2.013 2.040 22.660 2.067 2.080 22.754 2.1082.100 22.823 2.108 2.120 22.858 2.348 2.350 22.901 3.418 3.380 22.9613.794 4.122 23.004 3.507 3.588 23.038 3.358 3.316 23.081 3.234 3.19223.133 3.187 3.196 23.167 3.424 3.417 23.253 3.507 3.497 23.331 3.5873.581 23.408 3.353 3.351 23.503 3.292 3.300 23.580 3.344 3.330 23.6663.395 3.380 23.752 3.396 3.390 23.838 3.406 3.270 23.898 3.386 3.39023.993 3.509 3.478 24.079 3.576 3.586 24.165 3.530 3.401 24.242 3.5133.520 24.320 3.417 3.414 24.397 3.463 3.439 24.500 3.406 3.410 24.5863.399 3.400 24.664 3.241 3.290 24.750 3.272 3.280 24.836 3.322 3.28024.896 3.480 3.481 24.999 3.345 3.313 25.076 3.316 3.308 25.162 3.4793.479 25.240 3.491 3.509 25.343 3.544 3.525 25.395 3.373 3.405 25.4983.582 3.580 25.584 3.371 3.370 25.670 3.223 3.190 25.747 3.274 3.30025.833 3.518 3.500 25.919 3.414 3.409 25.997 3.445 3.451 26.074 3.4603.488 26.169 3.591 3.603 26.246 3.825 3.836 26.332 3.681 3.668 26.4013.392 3.372 26.487 3.395 3.380 26.573 3.404 3.390 26.667 3.320 3.30026.753 3.370 3.370 26.831 3.428 3.410 26.900 3.539 3.280 27.003 3.7313.723 27.080 3.498 3.476 27.158 3.572 3.552 27.252 3.349 3.361 27.2872.622 3.265 27.330 2.483 2.481 27.381 2.497 2.505 27.407 2.433 2.43827.467 2.140 2.170 27.510 2.047 2.050 27.536 1.920 1.920 27.579 1.8831.880 27.665 2.051 2.030 27.751 2.052 2.060 27.837 2.108 2.090 27.9062.066 2.060 28.009 2.153 2.150 28.086 2.136 2.140 28.164 2.096 1.13528.241 2.125 2.140 28.293 1.861 1.860 28.336 1.483 1.490 28.362 1.4731.620 28.405 1.472 1.470 28.465 1.482 1.500 28.508 1.486 1.470 28.5421.332 1.320 28.585 1.375 1.370 28.671 1.427 1.440 28.749 1.404 1.41028.835 1.313 1.310 28.903 1.380 1.380 28.998 1.331 1.340 29.084 1.3671.360 29.170 1.307 1.320 29.247 1.319 1.320 29.333 1.374 1.370 29.3941.261 1.250 29.505 1.216 1.220 29.574 1.229 1.220 29.669 1.227 1.23029.755 1.215 1.230 29.832 1.206 1.210 29.901 1.222 1.220 29.987 1.2051.210 30.082 1.347 1.350 30.125 1.221 1.240 30.168 1.177 1.180 30.2111.063 1.080 30.254 1.047 1.010 30.322 1.057 1.070 30.400 1.012 1.02030.503 0.987 1.012 30.580 0.943 0.932 30.666 0.889 0.902 31.707 1.2601.248 31.750 2.776 2.763 31.784 3.394 3.411 31.836 3.950 3.967 31.8794.110 4.098 31.905 3.968 3.969 31.956 4.140 4.110 32.017 4.019 4.04032.085 4.431 4.440 32.171 4.645 4.650 32.249 4.737 4.730 32.326 4.8274.840 32.404 4.756 4.754 32.498 4.212 4.182 32.576 3.953 3.975 32.6274.189 4.217 32.670 4.309 4.297 32.748 4.328 4.320 32.825 4.300 4.31532.902 4.338 4.366 32.997 4.263 4.270 33.049 4.225 4.230 33.083 3.9473.930 33.126 3.605 3.610 33.169 3.446 3.460 33.212 3.416 3.400 33.2463.511 3.530 33.332 3.503 3.520 33.401 3.387 3.380 33.496 3.327 3.34033.590 3.303 3.292 33.668 3.472 3.457 33.754 3.625 3.595 33.831 3.5443.520 33.900 3.603 3.626 33.986 3.551 3.570 34.081 3.618 3.610 34.1583.478 3.470 34.253 3.572 3.580 34.321 3.576 3.560 34.399 3.663 3.66034.493 3.596 3.609 34.588 3.312 3.331 34.665 3.238 3.261 34.751 3.3583.362 34.820 3.424 3.416 34.906 3.465 3.458 35.009 3.444 3.440 35.0873.450 3.470 35.164 3.474 3.470 35.250 3.485 3.510 35.328 3.627 3.63035.396 3.618 3.620 35.500 3.654 3.669 35.586 3.354 3.311 35.663 3.3893.404 35.749 3.463 3.452 35.835 3.550 3.544 35.895 3.449 3.484 36.0073.371 3.380 36.084 3.382 3.390 36.170 3.448 3.440 36.248 3.634 3.63036.334 3.743 3.730 36.403 3.633 3.630 36.506 3.376 3.382 36.583 3.3993.398 36.669 3.300 3.314 36.747 1.486 1.483 36.781 1.435 1.429 36.8151.283 1.296 36.858 1.293 1.306 36.919 1.394 1.390 36.962 1.404 1.42037.048 1.417 1.430 37.125 1.457 1.480 37.220 1.551 1.570 37.288 1.5711.570 37.366 1.571 1.540

[0164] Table 13 and FIG. 10 show the accuracy and precision of theon-line process over a long period of time, and a range of melt indexvalues. The gaps in the Figure indicate periods when the reactor wasdown. The horizontal regions indicate continued production of aparticular grade, and the steep vertical regions correspond totransitions between different grades. The data further show that theinventive on-line processes are accurate and precise even during gradetransitions. The 3σ accuracy of the predictions relative to the labvalues over the entire 5-week period was ±0.069 g/10 min.

[0165] Additionally, to test for model precision and long-term drift,the predicted MI of approximately 2200 samples of a particular grade wasmonitored for a static sample over a four-week period, in each of twocommercial-scale fluidized bed reactors. In each reactor, the datashowed a 3σ standard deviation of 0.012 g/10 min (for sample with meltindexes of 1.0 and 0.98 g/10 min; i.e., about 1%), and no measurablelong-term drift.

Example 9

[0166] Polymer density was predicted on-line along with the melt indexpredictions of Example 8, applying a density model to the same samplesand spectra as in Example 8. Nearly 300 samples were also tested thelaboratory, using the standard ASTM D1505 and ASTM D1928, procedure Cprotocol. The results, are shown in Table 14, where “ρ model” indicatesthe density predicted by the model, and “ρ lab” indicates the valueobtained in the laboratory by the ASTM method. The same data are showngraphically in FIG. 11, except that the Figure also shows the predicteddensity for samples not corresponding to lab measurements. The predicteddensity values are spaced sufficiently closely in time that they appearin the Figure to be a line. TABLE 14 Time ρ model ρ lab (days) (g/cm³)(g/cm³) 0.009 0.9173 0.9173 0.155 0.9183 0.9182 0.327 0.9176 0.91750.499 0.9175 0.9175 0.654 0.9172 0.9173 0.826 0.9178 0.9178 0.998 0.91730.9173 1.161 0.9173 0.9173 1.247 0.9167 0.9166 1.324 0.9169 0.9169 1.9950.9172 0.9172 2.159 0.9168 0.9168 2.339 0.9169 0.9168 2.511 0.91870.9186 2.580 0.9185 0.9184 2.666 0.9183 0.9184 2.838 0.9179 0.9180 3.0010.9166 0.9167 3.165 0.9173 0.9173 3.337 0.9172 0.9172 3.509 0.91810.9181 3.664 0.9173 0.9173 3.836 0.9173 0.9172 3.999 0.9165 0.9165 4.1710.9176 0.9177 4.334 0.9175 0.9173 4.498 0.9171 0.9172 4.670 0.91770.9175 4.833 0.9179 0.9179 4.997 0.9179 0.9178 5.177 0.9175 0.9176 5.3320.9172 0.9173 5.504 0.9177 0.9177 5.667 0.9173 0.9173 5.839 0.91710.9171 6.003 0.9166 0.9166 6.166 0.9169 0.9169 6.330 0.9179 0.9180 6.5100.9175 0.9175 6.665 0.9177 0.9177 6.854 0.9171 0.9170 6.949 0.91570.9157 7.000 0.9165 0.9165 7.086 0.9167 0.9167 7.164 0.9174 0.9174 7.3360.9179 0.9180 7.508 0.9182 0.9181 7.680 0.9179 0.9178 7.835 0.91780.9178 7.998 0.9175 0.9176 8.161 0.9173 0.9174 8.325 0.9168 0.9169 9.5030.9188 0.9190 9.580 0.9185 0.9185 9.666 0.9179 0.9181 9.752 0.91750.9174 9.830 0.9175 0.9174 10.002 0.9173 0.9174 10.165 0.9173 0.917110.329 0.9172 0.9173 10.501 0.9172 0.9173 10.664 0.9170 0.917 10.8360.9171 0.9171 10.999 0.9186 0.9186 11.085 0.9175 0.9175 11.163 0.91770.9177 11.249 0.9179 0.9179 11.326 0.9184 0.9183 11.507 0.9176 0.917711.670 0.9175 0.9173 11.834 0.9173 0.9172 11.911 0.9176 0.9175 11.9970.9173 0.9173 12.083 0.9180 0.9182 12.169 0.9181 0.9182 12.332 0.91860.9185 12.504 0.9172 0.9172 12.668 0.9167 0.9166 12.840 0.9165 0.916613.003 0.9173 0.9173 13.167 0.9176 0.9176 13.330 0.9176 0.9175 13.5020.9174 0.9172 13.674 0.9173 0.9174 13.837 0.9176 0.9176 14.001 0.91760.9175 14.164 0.9174 0.9175 14.345 0.9172 0.9170 14.500 0.9173 0.917314.663 0.9178 0.9179 14.826 0.9185 0.9183 14.998 0.9174 0.9173 15.1700.9172 0.9171 15.334 0.9171 0.9171 15.497 0.9174 0.9173 15.661 0.91700.9171 15.833 0.9171 0.9171 16.005 0.9174 0.9175 16.082 0.9171 0.917216.168 0.9176 0.9175 16.254 0.9181 0.9181 16.331 0.9180 0.9179 16.4950.9171 0.9171 16.667 0.9171 0.9169 16.744 0.9171 0.9169 16.830 0.91630.9163 16.994 0.9164 0.9164 17.166 0.9165 0.9163 17.329 0.9162 0.916117.501 0.9164 0.9164 17.664 0.9169 0.9169 17.836 0.9165 0.9167 18.0000.9175 0.9173 18.163 0.9168 0.9168 18.335 0.9170 0.9171 18.490 0.91680.9168 18.662 0.9176 0.9176 18.843 0.9172 0.9171 18.997 0.9181 19.0830.9176 19.169 0.9163 19.341 0.9163 19.505 0.9168 0.9168 19.582 0.91990.9199 19.660 0.9214 0.9214 19.746 0.9202 0.9204 19.832 0.9199 0.920019.995 0.9206 0.9206 20.167 0.9208 0.9207 20.330 0.9208 0.9206 20.5110.9207 0.9207 20.657 0.9203 0.9203 20.838 0.9215 0.9214 21.000 0.92060.9205 21.163 0.9208 0.9207 21.327 0.9211 0.9210 21.404 0.9186 0.918821.499 0.9170 0.9168 21.585 0.9168 0.9167 21.671 0.9172 0.9172 21.8340.9170 0.9170 21.998 0.9171 0.9171 22.084 0.9174 0.9174 22.170 0.91640.9164 22.247 0.9167 0.9167 22.324 0.9168 0.9167 22.496 0.9176 0.917722.660 0.9166 0.9167 22.823 0.9168 0.9168 22.901 0.9169 0.9168 23.0040.9175 0.9175 23.167 0.9184 0.9184 23.331 0.9180 0.9178 23.503 0.91770.9178 23.666 0.9175 0.9175 23.838 0.9174 0.9175 23.993 0.9182 0.918324.365 0.9184 0.9184 24.320 0.9172 0.9172 24.500 0.9175 0.9173 24.6640.9178 0.9178 24.836 0.9185 0.9184 24.999 0.9180 0.9181 25.162 0.91720.9172 25.343 0.9176 0.9175 25.498 0.9169 0.9170 25.670 0.9173 0.917325.833 0.9171 0.9171 25.997 0.9172 0.9172 26.169 0.9173 0.9173 26.3320.9172 0.9172 26.487 0.9172 0.9173 26.667 0.9173 0.9174 26.831 0.91730.9173 27.003 0.9174 0.9174 27.158 0.9164 0.9164 27.330 0.9173 0.917427.407 0.9162 0.9162 27.510 0.9162 0.9160 27.579 0.9169 0.9169 27.6650.9169 0.9168 27.837 0.9169 0.9168 28.009 0.9169 0.9171 28.164 0.91680.9169 28.241 0.9174 0.9173 28.336 0.9167 0.9168 28.405 0.9161 0.916028.508 0.9164 0.9164 28.671 0.9169 0.9168 28.835 0.9168 0.9168 28.9980.9164 0.9164 29.170 0.9167 0.9163 29.333 0.9169 0.9170 29.505 0.91640.9163 29.669 0.9171 0.9170 29.832 0.9173 0.9173 29.987 0.9174 0.917730.168 0.9165 0.9164 30.254 0.9172 0.9172 30.322 0.9170 0.9171 30.4000.9162 0.9162 30.503 0.9171 0.9173 30.666 0.9181 0.9180 31.750 0.92050.9205 31.836 0.9195 0.9195 31.905 0.9189 0.9188 32.017 0.9174 0.917632.171 0.9176 0.9177 32.326 0.9176 0.9175 32.498 0.9161 0.9160 32.6700.9171 0.9171 32.825 0.9175 0.9174 32.997 0.9171 0.9171 33.083 0.91700.9169 33.169 0.9171 0.9170 33.246 0.9170 0.9170 33.332 0.9170 0.917033.496 0.9175 0.9175 33.668 0.9174 0.9176 33.831 0.9168 0.9170 33.9860.9169 0.9168 34.158 0.9171 0.9170 34.321 0.9174 0.9175 34.493 0.91690.9170 34.665 0.9170 0.9170 34.820 0.9172 0.9171 35.009 0.9172 0.917335.164 0.9176 0.9176 35.328 0.9177 0.9176 35.500 0.9176 0.9176 35.6630.9183 0.9182 35.835 0.9169 0.9168 36.007 0.9166 0.9164 36.170 0.91740.9174 36.334 0.9169 0.9171 36.506 0.9172 0.9173 36.669 0.9169 0.916936.747 0.9162 0.9162 36.815 0.9162 0.9162 36.962 0.9172 0.9172 37.1250.9174 0.9172 37.220 0.9175 0.9174

[0167] Table 14 and FIG. 11 show the accuracy and precision of theon-line process over a long period of time, and a range of densityvalues. As in the previous Example, the gaps in the Figure indicateperiods when the reactor was down, the horizontal regions indicatecontinued production of a particular grade, and the steep verticalregions correspond to transitions between different grades. The datafurther show that the inventive on-line processes are accurate andprecise even during grade transitions. The 3σ accuracy of thepredictions relative to the lab values over the entire 5-week period was±0.00063 g/cm³.

[0168] Additionally, to test for model precision and long-term drift,the predicted density of the same approximately 2200 samples of Example8 was monitored for a static sample over a four-week period, in each oftwo commercial-scale fluidized bed reactors. In each reactor, the datashowed a 3σ standard deviation of 0.00006 g/cm³ (for samples withdensities of 0.9177 and 0.9178 g/cm³), and no measurable long-termdrift.

[0169] Various tradenames used herein are indicated by a ™ symbol,indicating that the names may be protected by certain trademark rights.Some such names may also be registered trademarks in variousjurisdictions.

[0170] All patents, test procedures, and other documents cited herein,including priority document U.S. Provisional Application No. 60/345337,are fully incorporated by reference to the extent such disclosure is notinconsistent with this invention and for all jurisdictions in which suchincorporation is permitted.

What is claimed is:
 1. A process for determining polymer properties in apolymerization reactor system, the process comprising: (a) obtaining aregression model for determining a polymer property, the regressionmodel including principal component loadings and principal componentscores; (b) acquiring a Raman spectrum of a sample comprisingpolyolefin; (c) calculating a new principal component score from atleast a portion of the Raman spectrum and the principal componentloadings; and (d) calculating the polymer property by applying the newprincipal component score to the regression model.
 2. The process ofclaim 1, wherein the step of obtaining a regression model comprises: (i)obtaining a plurality of Raman spectra of samples comprisingpolyolefins; (ii) calculating principal component loadings and principalcomponent scores from the spectra obtained in (i) using principalcomponent analysis (PCA); and (iii) forming the regression model usingthe principal component scores calculated in (ii) such that theregression model correlates the polymer property to the principalcomponent scores.
 3. The process of claim 1, wherein the regressionmodel is a locally weighted regression model.
 4. The process of claim 1,wherein the polymer property is selected from density, melt flow rate,molecular weight, molecular weight distribution, and functions thereof.5. The process of claim 1, wherein the sample comprises polyolefinparticles.
 6. The process of claim 5, wherein the step of acquiring aRaman spectrum comprises: (i) providing the sample of polyolefinparticles; and (ii) irradiating the sample and collecting scatteredradiation during a sampling interval using a sampling probe, whereinthere is relative motion between the sample and the sampling probeduring at least a portion of the sampling interval.
 7. The process ofclaim 1, wherein the polymerization reactor is a fluidized- bed reactor.8. The process of claim 1, further comprising: (i) obtaining a secondregression model for determining a second polymer property, the secondregression model including second principal component loadings andsecond principal component scores; (ii) calculating a new secondprincipal component score from at least a portion of the Raman spectrumand the second principal component loadings; and (iii) calculating thesecond polymer property by applying the new second principal componentscore to the second regression model.
 9. A process for determiningpolymer properties in a fluidized-bed reactor system, the processcomprising: (a) obtaining a locally weighted regression model fordetermining a polymer property selected from density, melt flow rate,molecular weight, molecular weight distribution, and functions thereof,the locally weighted regression model including principal componentloadings and principal component scores; (b) acquiring a Raman spectrumof a sample comprising polyolefin particles; (c) calculating a newprincipal component score from at least a portion of the Raman spectrumand the principal component loadings; and (d) calculating the polymerproperty by applying the new principal component score to the locallyweighted regression model.
 10. The process of claim 9, wherein the stepof obtaining a regression model comprises: (i) obtaining a plurality ofRaman spectra of samples comprising polyolefins; (ii) calculatingprincipal component loadings and principal component scores from thespectra obtained in (i) using principal component analysis (PCA); and(iii) forming the regression model using the principal component scorescalculated in (ii) such that the regression model correlates the polymerproperty to the principal component scores.
 11. The process of claim 9,wherein the step of acquiring a Raman spectrum comprises: (i) providingthe sample of polyolefin particles; and (ii) irradiating the sample andcollecting scattered radiation during a sampling interval using asampling probe, wherein there is relative motion between the sample andthe sampling probe during at least a portion of the sampling interval.12. The process of claim 9, further comprising: (i) obtaining a secondregression model for determining a second polymer property, the secondregression model including second principal component loadings andsecond principal component scores; (ii) calculating a new secondprincipal component score from at least a portion of the Raman spectrumand the second principal component loadings; and (iii) calculating thesecond polymer property by applying the new second principal componentscore to the second regression model.
 13. A process for controllingpolymer properties in a polymerization reactor system, the processcomprising: (a) obtaining a regression model for determining a polymerproperty, the regression model including principal component loadingsand principal component scores; (b) acquiring a Raman spectrum of asample comprising polyolefin; (c) calculating a new principal componentscore from at least a portion of the Raman spectrum and the principalcomponent loadings; (d) calculating the polymer property by applying thenew principal component score to the regression model; and (e) adjustingat least one polymerization parameter based on the calculated polymerproperty.
 14. The process of claim 13, wherein the step of obtaining aregression model comprises: (i) obtaining a plurality of Raman spectraof samples comprising polyolefins; (ii) calculating principal componentloadings and principal component scores from the spectra obtained in (i)using principal component analysis (PCA); and (iii) forming theregression model using the principal component scores calculated in (ii)such that the regression model correlates the polymer property to theprincipal component scores.
 15. The process of claim 13, wherein theregression model is a locally weighted regression model.
 16. The processof claim 13, wherein the polymer property is selected from density, meltflow rate, molecular weight, molecular weight distribution, andfunctions thereof.
 17. The process of claim 13, wherein the samplecomprises polyolefin particles.
 18. The process of claim 17, wherein thestep of acquiring a Raman spectrum comprises: (i) providing the sampleof polyolefin particles; and (ii) irradiating the sample and collectingscattered radiation during a sampling interval using a sampling probe,wherein there is relative motion between the sample and the samplingprobe during at least a portion of the sampling interval.
 19. Theprocess of claim 13, wherein the polymerization reactor is afluidized-bed reactor.
 20. The process of claim 13, wherein the at leastone polymerization parameter is selected from the group consisting ofmonomer feed rate, comonomer feed rate, catalyst feed rate, hydrogen gasfeed rate, and reaction temperature.
 21. The process of claim 13,further comprising: (i) obtaining a second regression model fordetermining a second polymer property, the second regression modelincluding second principal component loadings and second principalcomponent scores; (ii) calculating a new second principal componentscore from at least a portion of the Raman spectrum and the secondprincipal component loadings; and (iii) calculating the second polymerproperty by applying the new second principal component score to thesecond regression model, and wherein the step of adjusting comprisesadjusting at least one polymerization parameter based on the calculatedpolymer property, the calculated second polymer property, or bothcalculated polymer properties.
 22. A process for controlling polymerproperties in a fluidized reactor system, the process comprising: (a)obtaining a locally weighted regression model for determining a polymerproperty selected from density, melt flow rate, molecular weight,molecular weight distribution, and functions thereof, the locallyweighted regression model including principal component loadings andprincipal component scores; (b) acquiring a Raman spectrum of a samplecomprising polyolefin particles; (c) calculating a new principalcomponent score from at least a portion of the Raman spectrum and theprincipal component loadings; (d) calculating the polymer property byapplying the new principal component score to the locally weightedregression model; and (e) adjusting at least one polymerizationparameter based on the calculated polymer property.
 23. The process ofclaim 22, wherein the step of obtaining a regression model comprises:(i) obtaining a plurality of Raman spectra of samples comprisingpolyolefins; (ii) calculating principal component loadings and principalcomponent scores from the spectra obtained in (i) using principalcomponent analysis (PCA); and (iii) forming the regression model usingthe principal component scores calculated in (ii) such that theregression model correlates the polymer property to the principalcomponent scores.
 24. The process of claim 22, wherein the step ofacquiring a Raman spectrum comprises: (i) providing the sample ofpolyolefin particles; and (ii) irradiating the sample and collectingscattered radiation during a sampling interval using a sampling probe,wherein there is relative motion between the sample and the samplingprobe during at least a portion of the sampling interval.
 25. Theprocess of claim 22, wherein the at least one polymerization parameteris selected from the group consisting of monomer feed rate, comonomerfeed rate, catalyst feed rate, hydrogen gas feed rate, and reactiontemperature.
 26. The process of claim 22, further comprising: (i)obtaining a second regression model for determining a second polymerproperty, the second regression model including second principalcomponent loadings and second principal component scores; (ii)calculating a new second principal component score from at least aportion of the Raman spectrum and the second principal componentloadings; and (iii) calculating the second polymer property by applyingthe new second principal component score to the second regression model,and wherein the step of adjusting comprises adjusting at least onepolymerization parameter based on the calculated polymer property, thecalculated second polymer property, or both calculated polymerproperties.